Last week Dempster randomly bumped into a top Cubs executive on the street and had a casual conversation. Early this week the team had contact with Dempster and his representatives about his free agency.
"I don't want to treat Ryan any different than I would treat the other free agents," Cubs general manager Jed Hoyer said. "We talked about it last week, there has been contact, and I am sure there will be contact in the future, but I don't want (the media) to treat him differently. I am not going to comment on him and not comment on the rest of the (free agent pitchers)."
Dempster is coming off a four-year, $52 million contract he signed with the Cubs before the 2008 season. Entering his 14th major league season, Dempster, who will be 36 in May, was 12-8 with the Cubs and Texas Rangers in 2012.
He was traded to Texas in a deal that was consummated just minutes before the non-wavier traded deadline on July 31.
Although the relationship between Dempster and the Cubs was strained before he was traded, the two sides worked together to get a deal done with Texas. According to sources on both sides, the line of communication is positive as the process goes forward.
Dempster should have many suitors, but probably not the Chicago White Sox. He turned down a deal to the Sox twice before he was traded to Texas last season, according to a source with knowledge of the situation.
Another source said that the Milwaukee Brewers are in pursuit of Dempster, who has averaged over 200 innings for six straight seasons.