It’s that time again.

The trade deadline season typically takes on a bizarre life, in which information and misinformation are ladled in equal measure, usually with something as simple as an adverb or adjective. So it was on Monday night.

The Red Sox, reported ESPN’s Buster Olney, are “aggressive in the pursuit of Ryan Dempster,” the 35-year-old Cubs right-hander who is amidst a 33-inning streak without giving up a run that has him leading the NL in ERA (1.86).

Not so, a major league source told WEEI.com. The Red Sox have not been active in the pursuit of Dempster, as the team continues to survey the landscape of what is and isn’t available, and decide whether it a) represents an upgrade over what they have and b) comes at a tolerable acquisition cost.

What does that competing information mean for the reality of where the Red Sox stand regarding the pursuit of Dempster? Who knows? But how the Sox should proceed with regards to Dempster is another matter.

The Red Sox must (and will) explore options for upgrading their rotation. The team’s starters have a 4.71 ERA after Aaron Cook’s dazzling seven-inning performance in which he did not allow an earned run en route to Boston’s 5-1 win over the White Sox.

That mark ranks 26th among the 30 major league teams. The Sox aren’t going anywhere if their rotation doesn’t improve.

That said, the team has experienced some interesting developments in recent weeks, foremost the emergence of Cook and Franklin Morales. Cook, in four starts since coming off the disabled list, has forged a 1.67 ERA, an unbelievable (and, quite possibly, unsustainable) mark considering that he’s struck out just two batters in 27 innings. His turbo sinker has been tremendous, though it’s something of a leap of faith to think that he can dominate in start after start.

Nonetheless, if this is the same two-seamer that he had at his peak in Colorado – something that former Rockies teammate Morales insisted on Monday night was the case – then Cook has the potential to be a valuable asset to a rotation going forward. To this point, his 3.34 ERA is the best of any Red Sox pitcher as a starter this year.

The second-best mark on the team? That belongs to Morales, who has been mostly brilliant since his move to the rotation. He is 2-1 with a 3.42 ERA in five starts, having punched out an eye-popping 31 batters and walked just eight in 26 1/3 innings.

The net result of such performances is that the standard for upgrading the Red Sox rotation has gone up. The 4.71 ERA this year is one of the worst in baseball, but since May 26, the team has a 4.17 mark that is more of the middle-of-the-pack variety, thanks to both pitchers like Morales and Cook as well as improvement from Clay Buchholz and Jon Lester. In their last 270 innings, Sox starts have 227 strikeouts (7.6 per nine innings) and just 62 walks (2.1 per nine innings), ratios that suggest that the rotation is capable of performing at a very high level.

There will be pitchers on the trade market about whom the Red Sox have to debate long and hard. Matt Garza, a right-hander with a track record of tremendous success in the AL East who is in the middle of his pitching prime and will remain under team control through 2013, comes to mind.

There will be others who fit in that category, pitchers with the talent to make a difference and the years of control to justify (or at least come close to justifying) the prospect cost of sacrificing at least six big league seasons of cheap major league contributions.

But Dempster doesn’t fit either of those categories. He’s been a very solid starter for a number of years, forging a 58-44 record and 3.61 ERA with the Cubs since moving from the bullpen to the rotation on a full-time basis for the start of the 2008 season.

But he represents something of a siren on the trade market, a pitcher who has been dominant beyond his numbers and who is likely to endure a regression to his career norms sometime soon.

His stuff (at least as measured by fastball velocity; the once-hard-throwing right-hander now averages just under 90 mph on his fastball) is in a state of steady decline. Though he did have one excellent outing against the Red Sox -- tossing seven shutout innings against them in Wrigley Field on June 15 -- his lack of an overpowering arsenal would require a bit of a leap of faith to consider it an ideal fit or the AL East. His numbers are great this year, but he is living a charmed life, as the .244 batting average on balls in play that he’s allowed is drastically better than his .306 career mark.

In other words, while Dempster has been a very steady, solid pitcher for the Cubs during his tenure in their rotation, he comes with something of a buyer-beware tag. Though not quite as extreme an example, his availability on the trade market this summer is somewhat reminiscent of that of Jarrod Washburn in 2009.

The left-hander dominated for the Mariners in the first half, going 8-6 with a 2.64 ERA, but the marks seemed unsustainable based on the stuff, and he was the beneficiary of good fortune on elements like batting average in balls in play. As the Tigers discovered after trading for him, those numbers were, in fact, unsustainable. The pendulum of luck swung hard, and Washburn went 1-3 with a 7.33 ERA in eight starts for the Tigers.

The scenarios aren’t perfectly analogous, for a couple of reasons. Dempster’s track record of consistent success at this stage of his career is more established than was Washburn’s, who had been no better (and sometimes worse) than a league-average pitcher in the six years leading to his trade. Dempster’s better than that. Moreover, the acquisition cost for the Tigers ended up being insignificant, as neither Luke French nor Mauricio Robles (the players acquired by Seattle) has become a meaningful big league contributor in the subsequent years, and so the Tigers never had to regret the trade.

Dempster might be different, particularly in the world of the new Collective Bargaining Agreement that governs the game. He’s in the final year of a four-year, $52 million deal. Under the terms of the new CBA, the Cubs are in a position where they can make a one-year qualifying offer to him as a free agent after the season that represents the average of the top 125 salaries in the game.

This coming offseason, that figure will be roughly $12.5 million – a slight pay cut from what Dempster is getting this year. Given his performance this year, barring an injury or some either enormous red flag down the stretch, the Cubs can make such a qualifying offer with a sense of comfort that either Dempster will accept (and thus return on a short-term contract with which any team could be comfortable) or decline and, if Dempster leaves, collect a pair of draft picks.

But that won’t be the case for a team that acquires the veteran. Players must be with a team for an entire season in order to qualify for draft-pick compensation, meaning that if Dempster is traded, the team that lands him can’t get draft picks should he eave at the end of the year.

In other words, Dempster represents a pure rental, someone who can impact a pitching staff for roughly three months (perhaps into October) of this season, but no more. Yet in order to convince the Cubs to deal him, a team would have to offer Chicago something more valuable than the two draft picks that the Cubs could receive if they kept Dempster through the end of the year.

In sum: There’s going to be a high acquisition cost for Dempster, even though the return he can offer is brief and could be disappointing if he returns to earth from the lofty air in which he’s been traveling thus far this year.

Does the right-hander represent an upgrade to the Red Sox rotation based on what he’s done thus far this year? Of course. Is he likely to sustain his level of performance going forward? A bit murkier. If relocated from the NL Central to the AL East, would he be a better starter than Morales or Cook? Difficult to say – or, at the least, difficult to say he’d be a significant upgrade over what they’ve done. That being the case, would the Red Sox be willing to add him in spite of the likely hefty price tag that could (and, if you’re the Cubs, should) accompany his availability this summer?

Unless the Cubs don’t anticipate making a qualifying offer for the pitcher (perhaps out of concern that he would accept it, thus reducing their financial flexibility in the offseason), and thus won’t be holding teams to the better-than-two-picks standard, it’s hard to imagine the Sox’ interest aligning with the price.

That could change, of course. A couple of bad starts from Cook or Morales, or another shoulder scare from Josh Beckett, or continued less-than-stellar results from Lester, or evidence that Felix Doubront has hit a wall could all increase the Sox’ motivation for a deal. But for now, the idea that the team would part with some of the top talents in its system for a pitcher who would be no more than a rental seems a bit hard to fathom.