Kicker said that Munich’s supervisory board has approved the extensions and that a verbal agreement with the players has been reached.
The fan favourite and forward Mueller, 25, has been at Bayern since 2000 and his current deal is until 2019. He was a major target of Manchester United and their former Munich coach Louis van Gaal in summer but declared not for sale by Munich.
Defender Boateng, 27, came to Munich in 2011 from Manchester City and is contracted until 2018.
Kicker said that Mueller will become Bayern top earner with the new contract and Boateng would also see his salary considerably raised.