The Cleveland Plains Dealer is reporting that the Indians have made a claim for Thome and they now have to wait until 1 p.m. (et) Friday to see whether or not they get him.
Thome has a no-trade clause in his contract with the Minnesota Twins and must waive that in order to go to Cleveland.
The 40-year-old became the eighth player in history to reach 600 hundred home runs when he clubbed two against the Tigers at Comerica Park on August 15.
On the season, he is batting .248 with 12 homers and 40 RBI in 70 games for the Twins this season.
He came into the league in 1991 with Cleveland and played there until 2002. In his final year with the club, he hit a franchise-record 52 home runs and left the team with 334 home runs.
Thome then traveled to Philadelphia and played three years there prior to going to the White Sox until they traded him to the Dodgers during the 2009 campaign. He signed with the Twins prior to the 2010 season.
Over 2,462 games, he has belted 601 home runs and has driven in 1,664 runs while batting to a .277 average.