However, they would have to pay his salary, if they want him in the January window.
Arsenal have opened talks with the Bundesliga champions, in a bid to sign the Germany international this month.
Boateng has made just 15 appearances for Bayern this season.
The 31-year-old’s position at the club is currently under threat from Benjamin Pavard and David Alaba.
Arsenal’s head coach, Mikel Arteta, is searching for defensive options this January following Calum Chambers’ long-term injury.