The Germany legend feels the current Borussia Dortmund striker would be an "upgrade" on the striking options at the Allianz Arena and is eager for the club to sign him
Lewandowski is set to leave BVB on a Bosman move when his contract expires at the end of the season, with Bayern widely touted as the Poland international's ideal destination.
Although Mandzukic has proven a vital player for the European champions since his move to the club in 2012, Beckenbauer believes Lewandowski would prove a significant "upgrade" on the Croatia international.
"Regardless of how good Mandzukic is, Lewandowski will still be an upgrade," Beckenbauer was quoted as saying by Sport Bild.
"He is perhaps even stronger on the ball and his movement is even better.
"It would be great if he were to play for Bayern soon."
Lewandowski, 25, is currently leading the Bundesliga goalscoring charts with nine goals from 12 appearances and will be looking to add to his tally at the weekend when Dortmund host Bayern.
Mandzukic, meanwhile, sits second in the charts with eight goals from 12 games.