The German international - who has been with Bayern for the entire duration of his senior career to date - has been linked with a potential switch £37 million switch to Old Trafford in recent days, yet Beckenbauer is clearly not content with the thought of him departing the Allianz Arena.
"You shouldn't keep passengers, but they should fight to keep Thomas Muller if he has such plans," the 68-year-old - who has became synonymous with Bayern Munich during a glorious career in which he has featured as a player, manager and president for Bayern Munich - said in an interview with Bild that was quoted by Goal.com.
Muller has made over 150 appearances since breaking into the first-team setup at Allianz Arena and Beckenbauer - who captained his native Germany to World Cup success in 1974 - clearly believes that his departure should only arise if absolutely necessary.
"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."
Whether or not Muller will attempt to force a move to Manchester United remains to be seen. Although the 20-time English champions remain a significant attraction despite their lack of success this season, Bayern Munich have continued to dominate domestically under Pep Guardiola and Muller remains an integral figure.
However, if Louis van Gaal does indeed take the reigns at Old Trafford this summer as the long-term successor to David Moyes, Manchester United could become a more attractive proposition for Muller given that it was the experienced Dutchman who gave him his first chance to succeed with the Bavarians.
Manchester United fans - would you like to sign Muller? Is Beckenbauer right to suggest that Bayern Munich should try and keep him? Let us know your thoughts below.