According to sources, the Minnesota Twins are also interested in the free agent slugger.
Thome spent last season in Minnesota after signing a one-year, $1.5 million contract in February. He spent most of his time with the Twins as the designated hitter, hitting .283 with 25 homers and 59 RBIs in 276 at-bats.
Thome has played for five teams in his 19-year MLB career. The lefty became a star in Cleveland, helping the Indians supplant the Twins as the AL Central's top team in the mid-1990s.
After three years in Philadelphia, Thome returned to the division with the Chicago White Sox in 2006.
His solo homer in Game 163 in 2008 propelled the White Sox into the playoffs and sent the Twins home early for the winter. He was traded to the Dodgers late in 2009, but wanted to return to the White Sox in his home state of Illinois to finish his career.
The White Sox decided to go in another direction at designated hitter, so Thome wound up taking a deal with the Twins.
Information from The Associated Press contributed to this report.