Chelsea's strikers will love playing with Juan Cuadrado if he does join, says Thierry Henry.
Manchester United boss Louis van Gaal has said that Darren Fletcher's proposed move to West Ham is off.
The 23-year-old midfielder, a product of the Bavarian club's youth system, has put pen to paper on a new deal until June 2017.
"Thomas Muller came through the youth ranks at FC Bayern. We trained him here, and he's developed into a very important player for Bayern Munich," Bayern chairman Karl-Heinz Rummenigge told fcbayern.de.
"His contract ran until 2015 in any case, but we're delighted to extend that by two years until 2017 at this early stage.
"It's also proof of Thomas Muller's commitment to FC Bayern."
Muller, capped 38 times by his country, joined Bayern aged 11 and played at every youth level before making his Bundesliga debut in August 2008.
He became a first-team regular in the 2009/10 season and has performed superbly this term, scoring 13 goals and providing eight assists in 25 games in all competitions.