Yesterday’s 2-1 loss to the Cubbies at the Cell (y’think maybe Ozzie might wanna walk or knock down Alfonso Soriano in the first inning today?) dropped the White Sox to 29-41, 13 1/2 back of the Tigers (beneficiares of another Justin Verlander gem yesterday against the squabbling Braves and ejection-happy Bobby Cox). As such, the Chicago Sun-Times’ Joe Cowley suspects ChiSox GM Kenny Williams is leaning towards a rebuilding mode.

According to a source close to the situation, negotiations between the Sox and Mark Buehrle’s camp have been exhausted, with Williams believing he has no choice but to trade the left-hander, who is the face of the ballclub.

At least seven teams have made serious contact with Williams, with three actually having the resources to pry Buehrle from the White Sox. The Atlanta Braves and New York Mets were the leading contenders until this weekend, with the Boston Red Sox now becoming the front-runner.

While Williams wouldn’t acknowledge that Saturday, he didn’t have to. Allard Baird, the Red Sox’ assistant to the general manager, was in town Friday to watch the White Sox’ loss to the Cubs — in which Buehrle started — and reportedly was to be sent out on assignment only when things were about to get serious.

According to the source, the Red Sox not only want to keep Buehrle away from the New York Yankees and are willing to offer him a contract extension in the five-year range he is seeking, but they have a farm system loaded with players in whom the White Sox are interested.

Starting pitchers Clay Buchholz and Michael Bowden are on the White Sox’ radar, as well as speedy outfielder Jacoby Ellsbury and shortstop Jed Lowrie.

Williams wants to make sure every offer has been heard before pulling the trigger on a decision that could be a public-relations disaster — but also one Williams believes he has no choice but to make. A recent look at the White Sox from top to bottom has shown the GM that the farm system basically has been a failure.

That’s the main reason the decision was made Friday to fire Duane Shaffer, who had been in charge of the draft since 1991.