The Germany international says it is no secret that he enjoys an excellent rapport with the Dutchman but has made it clear that he is happy at the Allianz Arena.
The Germany international became a first-team regular during the Dutchman's spell at the Allianz Arena between 2009 and 2011 and he has not forgotten about his former mentor.
"It's not a secret that Louis van Gaal and I have a relationship that goes a bit further than a normal trainer-coach relationship," Muller was quoted as saying by Sport Bild when questioned about the new United boss.
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Nevertheless, the 24-year-old has insisted that he is happy in Bavaria and is not thinking about a transfer just yet.
"I have a contract with Bayern Munich until the summer of 2017," Muller pointed out. "I really enjoy playing for Bayern. There's not really anything better than this."
Muller played a key role in the Allianz Arena side's domestic double this term, scoring 13 goals in 31 Bundesliga appearances, while netting eight times in five DFB-Pokal games.