The Johnny Damon Sweepstakes appeared to be nearing the finish line Thursday, as Damon tries to choose from several offers far less than the two-year, $20 million deal he and agent Scott Boras have been seeking. Two sources told ESPN.com that the Detroit Tigers have made the largest offer, amid speculation around the industry that that bid is in the range of one year, $7 million. There were indications the sides were still discussing a possible two-year deal. But even the Tigers' one-year offer appears to be the biggest offer on the table. The Atlanta Braves and Tampa Bay Rays have also remained in the bidding, with both teams talking about one-year contracts for fewer total dollars than the Tigers' offer. MLB.com reported that the Braves' offer was for less than $4 million. A source indicated the Chicago White Sox also have expressed late interest.