Manchester City would be interested in signing Raheem Sterling if he were to become available, according to Sky sources.
Tottenham have completed a deal for Cologne defender Kevin Wimmer and he will join them in June, Sky sources understand.
The 30-year-old Frenchman announced after winning the treble with Bayern last season that he had agreed to sign a new deal with the record German champions.
Now, following the first two days of pre-season training, he sat down to rubberstamp his commitment by signing on the dotted line.
"I'm really pleased," he told the club's official website. "I always said how great it feels to be at FC Bayern.
"I have a good feeling for me and my family and I hope things will carry on the way they were in the past year."
The 72-time France international joined Bayern in 2007 from Marseille and soon became a hit in the Bundesliga.
He has won three Bundesliga and DFB-Pokal titles and the Champions League for Bayern.