The 68-year-old believes the Bundesliga champions would be foolish to let the Germany international leave the club at the end of the season
The 24-year-old is among the players tipped to join Old Trafford this summer, while Bayern chairman Karl-Heinz Rummenigge has refused to rule out the forward's departure.
"You shouldn't keep passengers, but they should fight to keep Thomas Muller if he has such plans," Beckenbauer told Bild.
"He is an established figure under Pep Guardiola. So they should do everything possible to keep Muller. They should only look for another solution if he refuses categorically."
Bayern face Borussia Dortmund in the DFB Pokal final on May 17 and Beckenbauer says Robert Lewandowski should not try too hard to impress his new club ahead of his summer move to the Allianz Arena.
"He should not overdo it," he continued. "BVB have long had their weaknesses."