Bayern are in the market for a replacement for new Juventus signing Andre Pirlo and are considering the Germany international.
A bid for €25 million is being prepared for Schweini, who has confessed his admiration for Milan.
“Milan are a great club,” the player has said. “Never say never, so we’ll just have to wait and see.”
Milan’s other midfield options are believed to be Fiorentina’s Riccardo Montolivo and Alberto Aquilani of Liverpool.