Konerko, Thornton fans of Dempster

Ryan Dempster probably wouldn't mind the idea of staying in Chicago with his family. Dempster Family Foundation

The Chicago Cubs are working toward moving Ryan Dempster to a contender, and if that results in Dempster being able to stay in Chicago with the surprising White Sox, at least two South Siders would welcome him to the clubhouse.

And with three children all under the age of six, Dempster may like the idea of sticking around.

"Demp is a great, great guy and we would have fun talking some hockey together," Sox captain Paul Konerko said. "He is going to make any team he gets traded to a lot better. He is a big-time, front-line starter, but I have a feeling there will be a ton of suitors and for him, and some teams may go above and beyond what we can."

Cubs president Theo Epstein, who is looking to build for the future by acquiring young talent, had a conversation with the 35-year-old Dempster on Wednesday.

"We discussed a lot of things and obviously there are a lot of things being talked about," Dempster told ESPNChicago.com of the meeting that took place in the Wrigley Field grandstand before Wednesday's game against the Detroit Tigers. "We talked about being on the same page and trying to do what is best for our team."

With Gavin Floyd and Philip Humber struggling, White Sox GM Kenny Williams and his staff are looking for another starter and a third baseman. Chemistry is always a major issue when a club looks to add a player in midseason.

"I know Kenny, he is always looking to add on," Konerko said. "That said, there is a good vibe in our clubhouse with the guys we have, and how do you make a case for someone to be replaced?"

Dempster may be the type of pitcher that you make an exception for considering the clubhouse credibility he brings as well as a 2.31 ERA.

"If they are going to bring in an unselfish guy that will make our team better so be it," Sox reliever Matt Thornton said. "We trust our front office to do that and add talent at the same time.

"You know of Ryan through his reputation -- a great teammate an d a great pitcher as well as a good person. Whoever does get Ryan Dempster is going to be pretty happy with what he brings to that team."

The Cubs will not be shy in asking top pitching talent in return for the veteran pitcher, and it remains to be seen if the White Sox would consider moving any pitching off of their 25-man roster.