11:06pm: Mark Gonzales of the Chicago Tribune hears from a team source who says he can imagine Damon signing with the White Sox. "I think we have a good shot to get him now," the source said.
Another person discounted the importance of Damon's recent golf outing with Pierzynski and Harrelson.
6:26pm: Joe Cowley talks to Pierzynski about the Damon negotiations, and Cowley quotes an unnamed member of the White Sox who says "I would be surprised if [Damon] didn't sign with us.''
4:13pm: Rosenthal tweets that the present-day value of Chicago's offer to Damon is in the $4.5MM range, considering deferrals. He's hearing that Damon doesn't want to go to the Tigers. As for Damon's wife's preferences, the player texted to SI's Jon Heyman that "It's up to me. She's going wherever I go." Cowley tweets that the Sox "are going from long shots to frontrunners in the Damon sweepstakes the last few hours."
12:02pm: Rosenthal wrote yesterday that "some with the White Sox are confident that a deal with Damon could happen, and believe it might even be close." Similarly, Joe Cowley of the Chicago Sun-Times writes today that "the White Sox front office is feeling like they may have 'significantly' closed the gap between themselves and Detroit for the free agent's services." However, Cowley has one source that still considers the Tigers the frontrunner. Also, Scot Gregor of The Daily Herald believes the Braves are still in the mix.
8:50am: Yesterday we heard from Ken Rosenthal of FOX Sports that free agent Johnny Damon played golf Monday with White Sox catcher A.J. Pierzynski and broadcaster Hawk Harrelson. The Sox remain firm on their initial offer, one that could be slightly above $4MM according to Mark Gonzales of the Chicago Tribune. SI's Jon Heyman tweeted this morning that White Sox owner Jerry Reinsdorf recently got involved in the Damon talks. Gonzales notes that the White Sox-Scott Boras relationship appears to be thawing, given the Damon talks, the Andruw Jones signing, and the Sox drafting a Boras client in the 16th round of last year's draft.
Meanwhile, Lynn Henning of the Detroit News says the Tigers and Damon "appear to be moving, at less than full speed, toward a deal." It seems that one of these two clubs will sign Damon, but it's difficult to peg a frontrunner.