Germany legend Beckenbauer also hailed Rooney as the best player in the world, along with Barcelona's Lionel Messi, and said the striker could inspire England to World Cup glory in South Africa this summer.
But stopping Rooney adding to his tally of 33 goals already this season in next Tuesday's clash in Germany, followed by the return at Old Trafford on April is Beckenbauer's immediate priority.
Simply the best: Franz Beckenbauer says Wayne Rooney's form this season for Manchester United has seen him join Lionel Messi as the world's top footballers
'Rooney is doing an absolutely fantastic job for Manchester United,' said Beckenbauer. 'I must tell you that we at Bayern will fear him when we play United in the Champions League quarter-finals.
'He is a brilliant player who is playing better than ever. It's not easy to score 33 goals for your club in England, or anywhere else.'
Beckenbauer also admitted both he and Bayern are still smarting after United snatched the 1999 Champions League from the Germans' grasp with two injury-time goals - and that revenge is most definitely on their minds.
'Of course we would like to knock them out for revenge for losing the 1999 final, but it's going to be tough,' said Beckenbauer.
Hot shot: Rooney scores his 33rd goal of the season against Liverpool
'And, of course, United have Rooney. Anything is possible but first we have to stop Wayne and no-one has been able to do that very often this season.'
'The Kaiser', who has won the World Cup with Germany both as a player in 1974 and as coach in 1990 also talked up the chances of old enemies England at the World Cup finals this summer and insists Rooney could be the key to a first success since 1966.
'If he continues scoring like that and playing like that he can win the World Cup for England,' said Beckenbauer.
'I think England will go to South Africa among the favourites alongwith Spain, Brazil and Argentina because, of course, Argentina haveLionel Messi.
Still hurts: Bayern Munich will be motivated by Manchester United's 1999 Champions League win in next week's clash, says Beckenbauer
'Along with Rooney, he is the best player in the world right now.They are different players because Messi is so fast and imaginative,while Rooney is so strong.
'But Wayne has made the biggest improvement to his game. He haschanged the way he plays and, at 24, has added a maturity to his game.
'Playing as the front man, he makes it so hard for defenders to markhim and he's able to use the crosses from both wings so well.
'I have never seen him play better and I have been watching him for a long time now.'
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