The 30-year-old has often found himself on the bench this season behind Philippe Coutinho, who Bayern coach Niko Kovac prefers in the attacking midfield role.
According to Kicker, Inter’s “interest is intensifying” and the Italian giants could bring Muller to Milan in the January transfer window.
Mueller made a rare start, only his fifth of the season, in Tuesday’s 3-2 win at Olympiakos in the Champions League on the right wing, helping set up two goals for Robert Lewandowski.
“I’m trying to concentrate on playing football. Slowly all the discussions will come to an end,” Mueller told reporters in Athens when asked about his future at Bayern.
He has spent his entire career at Bayern, who he joined as a schoolboy in 2000, and club president Uli Hoeness has made it clear that no one at the club wants to see Mueller leave.
It has been a difficult year for Mueller, who was told by Germany coach Joachim Loew in March, alongside fellow 2014 World Cup winners Mats Hummels and Jerome Boateng, that he has no future in the national squad.