The German international recently extended his contract at Allianz Arena until the summer of 2024, meaning he is expected to remain a one-club man throughout his trophy-laden career.
The 32-year-old has won the most trophies of any other German international in the history of the game having surpassed Bastian Schweinsteiger's record of 26.
Muller revealed that he considered an exit from the team on three occasions - including once when United came calling with a major monetary bid under former Bayern boss Louis van Gaal.
"Bayern clearly rejected the whole thing - despite this insane offer from United," Muller told Merkur.
"[But it was a] huge vote of confidence from Bayern."
"It was relatively close at the time. Luckily, looking back, [Bayern Munich II boss] Hermann Gerland fought back with all his might and prevented the transfer."
The German attacker almost left once more recently after growing concerned over his direction under Niko Kovac - having fallen down the pecking order under the manager.
"Since I didn't get the playing time that I would have liked to have in this phase, I sought a conversation with the club about all the possibilities."
Muller, however, has not ruled out a potential exit or other options beyond the end of his current contract.
"I'll push that back,' he added. 'I feel good about it, don't feel any pressure and have a wide variety of options."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!