
"Mourinho? Why not? He could do a language course by the summer," Beckenbauer said in an interview with Bild newspaper Friday.
However the former World Cup winning coach and captain of Germany said he could also imagine some other candidates for the job of leading Germany's most successful side.
Beckenbauer did not mention any names but said: "He has to be shrewd tactician, to have already gained experience and to have command of the German language. Our team needs a high-class coach."
Mourinho, who won the Champions League with Porto before joining Chelsea, would fit the bill if he learned German.
He is been out of contract since leaving Chelsea in September and is thought to be interested in coaching a leading European club. He has already turned down the chance of coaching England.
Beckenbauer said he was in no doubt that Hitzfeld would "give everything" for Bayern for the rest of the season.
"The players will themselves have to answer the question of character in the next few months. I hope we get the right answer," he said.
Hitzfeld said this week he would not be extending his contract at Bayern which runs until June 30 this year.
"For Ottmar Hitzfeld the decision has a good aspect: he no longer has to take anything or anyone into account.
"The only disadvantage is that we now have daily speculation as to his successor which could cause unrest in the team."
Beckenbauer said there was still plenty of time to find a coach. However he conceded it would be difficult to include him in the management's planning if he were still under contract at another club.
The initial shortlist will be drawn up by chairman Karl-Heinz Rummenigge and general manager Uli Hoeness before final approval is given by the supervisory board.
DPA