Gonzalez could help the Indians settle their outfield situation, which became muddled following the club's decision not to re-sign All-Star Michael Brantley and other moves.
The 33-year-old Gonzalez spent 10 seasons with Colorado and was one of the team's best players and emotional leader. He left the Rockies after 2017 before re-signing with Colorado last March to a one-year, $5 million contract.
If he makes Cleveland's 40-man roster, Gonzalez will get a $2 million contract in the majors. He can earn $1 million more in bonuses.
A .287 career hitter with 231 home runs, Gonzalez was streaky last season when he batted .276 with 16 homers and 64 RBI. Gonzalez hit 40 homers in 2015, and he might be able to help Cleveland offset the loss of slugger Edwin Encarnacion.