The Germany international has been linked with a move to Manchester United this summer and club CEO Karl-Heinz Rummenigge hinted that the 24-year-old could be sold.
However, Beckenbauer believes that the Bavarians would be stupid to let the attacker leave for Old Trafford.
"You shouldn't keep passengers, but they should fight to keep Thomas Muller if he has such plans," he 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."