If he continues the way he has, there's no reason a half-dozen teams wouldn't be clamoring for his services. Starting pitching has been one of our bright spots this year and Dempster has certainly bounced back from a down year.
What's nice is that potential suitors know exactly what they're going to get from him -- a quality veteran with a good clubhouse presence, and an innings eater than can strike guys out. As others have mentioned, he's also going to be a free agent. He'll likely be pitching for his last contract and a solid performance could get him a three-year deal for a team looking for a fourth or fifth starter.
As for teams who will be searching for starters -- the Yankees and Red Sox are obvious choices, especially the Red Sox. Dempster could also get looks at surprise teams who're still in the running around the trade deadline. A team like Toronto, the Mets, Baltimore or Arizona could be looking to add depth if they choose to become buyers in July.
I'd be happy with getting one B-tier prospect and a few serviceable projects. My top choice would be a team like Toronto, who has plenty of quality pitching and outfield prospects. A package of RHP Deck McGuire, 3B Matt Dean and RHP Chad Jenkins would be a fantastic haul for Dempster.
McGuire is nearly ready for the big leagues. He's a big guy (6'6'' 240) with lots of experience. He may have a lower ceiling than some other prospects, but a lot of the stuff I've read about him projects to be a solid #3 or 4 starter. Dean is a converted shortstop who was a second team All-American at Texas. Jenkins, much like McGuire, is viewed as a "safer" prospect who will likely shift to the bullpen when he's called up.