MILWAUKEE -- The Chicago White Sox have not ruled out the chance of bringing back Mark Buehrle, but for the first time this offseason general manager Kenny Williams didn’t sound optimistic that it would happen.

It wasn’t as if Williams said Buehrle is gone. He tried to remain positive during the first day of the general managers' meetings in Milwaukee. But without being prompted, Williams also talked about what life would be without the popular left-handed veteran, and he became reflective.

“He has been as consistent of a performer as you’d ever want over the time he’s been here,” Williams said of Buehrle, who has posted 11 consecutive seasons of double-digit victories, 200-plus innings and 30 or more starts. “What I will miss more than that is the person he is. And you guys know what I’m talking about.

“When you talk about teammates, good teammates, supportive teammates, guys who have fun in the game, know when to be serious, know when to check somebody but know when to make somebody laugh, this is the guy you want. There’s much more that we’re going to miss than just every-fifth-day from Mark.”

The White Sox are trying to follow the same scenario that led to Paul Konerko returning last offseason. They are essentially letting other teams set the market for one of their players and then deciding if he fits into the budget.

But there are clearly more big-money teams interested in paying big bucks for a innings-eating left-handed starter than there were for a slugging first baseman last year.

“Listen, it’s no secret that he’s been sought after so he has options. And I don’t have the details just yet what those options are, but he has options,” Williams said.

The Rangers, Yankees, Red Sox and Marlins have all been reported to have interest in Buehrle. The White Sox’s biggest competition for Konerko last season came from the Diamondbacks.

But it wasn’t just the decision to re-sign Konerko that has left the White Sox without the funds to sign Buehrle. Big contracts for guys like Adam Dunn and Alex Rios, who both struggled mightily last season, have left the White Sox with a thin budget after giving them a struggling club that fans elected to not support in 2011.

Williams continued to say Monday that he doesn’t blame the fans for not coming out to see a team that even he found difficult to stomach.

“So if it comes down to 'he’s not here,' we got to make the adjustment,” Williams said. “That’s just the business of baseball. But it doesn’t mean we like it. It doesn’t mean that’s our preferred course. It doesn’t mean we won’t want him here. Just means this is kind of the way it has to be.”