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. The Chicago White Sox also have expressed interest, as ESPNChicago.com reported late last month.

At this point, if Damon landed with any team other than the Tigers or Braves, it would be a surprise. He and Boras have been publicly expressing their admiration for both teams. And both, conveniently, hold spring training close to Damon's home in Orlando.

Officials of both the Tigers and Braves declined to characterize their offers or the state of their negotiations Thursday. However, speculation in the industry, from people who have spoken with various principals, is that Damon will make a decision by the end of the week.

Jayson Stark is a senior writer for ESPN.com.