Boateng, 30, has appeared increasingly unhappy at Bayern this season, after losing his place in the team to Niklas Suele.
Having remained on the bench as Bayern won the German Cup final on Saturday, Boateng immediately disappeared down the tunnel after the final whistle, and did not join his team mates' on-pitch celebrations.
"I would advise him to leave the club. I think he needs a new challenge," Bayern president Hoeness told Bavarian broadcaster BR on Sunday.
"He looks out of place. As a friend, I would advise him to find a new club."
The 2014 World Cup winner's current contract at Bayern expires in two years, and he has recently been linked with a move to Inter Milan or Paris Saint-Germain.
Boateng came close to a move to the French club last year, telling Die Welt newspaper he had held "good conversations" with PSG coach Thomas Tuchel.
The transfer ultimately fell through, however, with Bayern sporting director Hasan Salihamidzic accusing the French club of "peculiar tactics".
Along with Mats Hummels and Thomas Mueller Boateng was told by Joachim Loew in March he would no longer be selected for Germany.