CHICAGO -- The ongoing debate as to whether Jermaine Dye and/or Scott Podsednik have played their last innings for the White Sox, and as to whether favorite son Jim Thome has a chance to return as the White Sox designated hitter will be just that.

Ongoing throughout the Hot Stove period of the current offseason.

"It's November 9th or 10th or whatever today is. Who knows?" said White Sox general manager Ken Williams, before making a quick exit from the General Managers' Meetings at the O'Hare Hilton on Wednesday. "All you can do is have conversations. It's the same thing every year at this time of year.

"So, there is nothing to report. Even if there was something to report, I wouldn't tell you."

Williams was true to his word during Wednesday's brief conversation. He wouldn't comment as to whether any team had asked about closer Bobby Jenks' availability during these GM Meetings and answered with a simple "Yes" when asked if it was harder in this present climate to make trades where young prospects come back in return.

Although the budget Williams has to work with for 2010 has been placed at a set figure without much wiggle room, Williams admitted to playing with that number a bit during the Meetings.

"[White Sox chairman] Jerry [Reinsdorf] gives you a pretty hard number, but we're working on him," Williams said. "Yeah, but I always work on changing it. I think I'm becoming annoying to him, actually."

As for the White Sox free agents, Dye admitted in interviews with the Chicago Sun-Times and Chicago Tribune how a chance existed, albeit remote, that he could return to the White Sox. But he also is realistic about the money the White Sox have to spend, not to mention his desire to play right field or first base, pushing him further out of the team's picture.

Podsednik and the White Sox remain apart in negotiations on his overall value. The prevailing school of thought is that if Podsednik gets what he wants, a multi-year deal, then he will not return to the White Sox in 2010. If his asking price is not met and the White Sox have not moved on at the leadoff spot at that point, then Podsednik still could come back.

Negotiations continue between the two sides, although relatively unchanged from over the weekend. It's too early, though, for Williams to remove anyone from White Sox consideration.

"I know which direction I want to go, but I can't exclude anyone," Williams said. "I could tell you the likelihood with each day that goes by is not great.

"But at the end of the day, when January comes around, you can be looking around and there is going to be some opportunities. The end of December or January, so you got to wait to play your hand."