Khedira has been linked with a move to Bayern since the end of the Euros.
"He is the player that Bayern need," Beckenbauer-old told TZ.
"He is a world-class player, as he demonstrated for Germany at Euro 2012. In Madrid he has matured into a true leader. There are very few players with his characteristics today.
"Bayern have quality players, but sometimes they only give 70 or 80 per cent on the pitch and that's not enough.
"The fans want to see people giving 100%. Khedira is one of these guys that have a lot of character. He is someone that Bayern need so much, but you don't get players like Khedira easily.
"The fans ask all players to play like [Lionel] Messi, but there is only one Messi. Khedira is the prototype of player willing to sacrifice himself for the team.
"How many players are willing to do that today? Who struggle and fight selflessly for the benefit of their peers? Those are the questions that need to be answered."