Brantley, after missing most of the 2016 and 2017 seasons with injuries, hit .309 with 17 homers and 76 RBIs this year. He scored 89 runs in 143 games and posted an .832 OPS.
Several teams were scouting Brantley heavily at the end of the regular season.
Cleveland president Chris Antonetti said the team is interested in re-signing Brantley but did not want to commit $17.9 million for one year.
"We could not have any more respect for any individual than we have for Michael," Antonetti said. "He's the guy that epitomizes, as I've shared before, all of the things we look for in a player. He's exceedingly productive on the field. He defines professionalism in the clubhouse, and he's an extraordinary teammate. The interest and desire is there. What we will have to work through is can we make the pieces fit?"