"The Milan directors have been keen to show their interest in me regularly over the last six years," he told L’Equipe.
"I still have two years on my contract, but I will pay close attention to what happens over the next few days."
"I am proud to get Milan’s attention, but my first priority remains Bayern Munich."
The France international has not been playing regularly under Ottmar Hitzfeld this season, but could retrieve his starting role amid the arrival of Jurgen Klinsmann.
"I have spoken to the new coach Klinsmann and he told me that he is counting on me," said the 31-year-old full-back.
"Nonetheless, in the world of transfers, things can go very quickly. Milan are a big club and there is another great team, who aren’t Italian, that are taking an interest.
"All I can say is that I will make my decision before the European Championship. For now, I just want to concentrate on playing."
Milan, who have just signed Mathieu Flamini from Arsenal, are looking to reinforce the squad after a disappointing season in Italy and Europe.