The dynamic midfielder has been linked with a move away from Madrid and the ex-Germany star would welcome him with open arms at the Allianz Arena
Khedira has recently been linked with a return to Germany, while Arsenal and Chelsea are also keeping tabs on the midfielder's situation as his future at Madrid remains uncertain.
Last month Goal revealed both Arsenal and Chelsea were pursuing the 27-year-old, but the player's £200,000-a-week wage demands prevented an agreement being reached with either.
Beckenbauer believes the midfielder would be a great addition to the Bayern squad and would be a suitable partner for Bastian Schweinsteiger or Philipp Lahm.
"Khedira would fit in in any team. He would fit in very well at Bayern, too," Beckenbauer was quoted as saying by Sport Bild.
"He is incredibly strong in the No.6 position. He could play alongside Philipp Lahm or Bastian Schweinsteiger. That would be perfect.
"It doesn't matter that he lacks a bit of speed. In midfield, it's all about the willingness to run rather than about speed."
Khedira joined Madrid from Stuttgart in the summer of 2010 and has since made close to 100 La Liga appearances for the Santiago Bernabeu side.
He faces stiff competition for places in midfield, though, with Xabi Alonso, Luka Modric, Illarra and Toni Kroos all capable of playing in his position and could therefore be on his way out of Madrid.
The 27-year-old has a contract at the Bernabeu until June 2015.