Dempster, who is in the final season of a four-year contract that pays him $14 million in 2012, is trying just to focus on what he can control: his performance on the mound.
"I think I would be doing everybody in that locker room and anybody who is a Cubs fan and most importantly the Cubs organization a huge disservice if I didn't put all my focus and attention on trying to make my start and do the best I can to help us win," Dempster said Wednesday on "The Waddle & Silvy Show" on ESPN 1000. "You're in a situation where if it does happen, they are going to do what's best for the Chicago Cubs, and I'm all for that."
The 35-year-old Dempster has full no-trade rights as a player with at least 10 years of major league experience and five with the same team. He might be a luxury for the 19-36 Cubs, who are rebuilding under new team president Theo Epstein and general manager Jed Hoyer, and likely would not be in their future next season as a free agent, anyway.
If the Cubs are planning on dealing Dempster, he certainly is helping to drive up the price. He ended an improbable run of 19 starts without a victory Tuesday with seven shutout innings in the Cubs' 10-0 victory over the Brewers. A lack of run support from the Cubs, who rank 14th in the NL in runs scored, has played a big role in his 1-3 record. But Dempster's 2.59 ERA ranks 10th in the National League.
"I've been playing long enough now that those kind of things don't bother me as much maybe like they would when you were younger," Dempster said. "You kind of get a lot of emotions going, but I've been playing in Chicago for a long time. It's a weird thought to be playing somewhere else, but it's also a possible reality. Whatever ends up being I'm just focused on going out there on Sunday and beat the Minnesota Twins."
With Epstein and Hoyer focused on this week's draft, their attention likely will shift to potential deals for Dempster, pitcher Matt Garza and others on the roster before the July 31 trade deadline.
"We always just talk. It's been more, 'Hey, maybe we'll have some talks about what's going on,' " Dempster said of Epstein and Hoyer. "They've put a lot of hard work into it, hitting it head on and have been determined to do what they have to do there. I'm sure that those conversations might come up down the road, they might not. I'm not quite sure."
In his ninth season with the Cubs, Dempster had some fun when asked if he would consider a trade to the White Sox, who are in first place in the American League Central.
"I don't know, was there a team 10 miles south of us?" Dempster joked. "That's a question I can't answer. I don't know what direction they want to go, I don't know any of those answers. Whatever it ends up being, I'll have to take a look at it and see what's the best for me, best for the Cubs and I respect that and I understand that.
"Hopefully I'm here, but if not it's somewhere that can ultimately give them the best opportunity to improve the Cubs for the future. I believe I'm a part of that and trying to help us for the future and help us for the present as well."