The Bavarians have reached three of the last four finals, arch rivals Borussia Dortmund in the 2012-13 final at Wembley in May.
However, the ex-Germany star does not think they can repeat the feat this term, also dismissing Jurgen Klopp's side's chances of reaching another showpiece.
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"The likes of Barcelona, Real Madrid and Manchester United are big threats who I think will get there instead."
The 45-year-old also gave his opinion on a number on the summer's transfer dealings, saying it was impossible to justify Gareth Bale's €100 million (£85m) move to Real Madrid and backing Mesut Ozil to shine at Arsenal.
"A transfer of €100m is crazy," he insisted. "I feel sorry for the boy because it is almost impossible to justify this money. Sometimes the fun is lost in football.
"With Ozil, I can see why Madrid went through with the move. The bottom line is that he is an outstanding footballer who will prevail in England."
Finally, Effenberg heaped praise on Dortmund star Marco Reus, who has impressed during BVB's blistering start to the season.
"The player I am fascinated in at the moment is Reus," he admitted.
"He has incredible quality, and when he is substituted for Dortmund I actually get angry because I want to keep watching him play."