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The Liverpool forward has become a global superstar in recent years and is one of the most popular figures in Egypt.
He's helped the Reds to Premier League and Champions League glory since arriving in 2017 and Rummenigge thinks he is up there with the best.
"In my opinion, Salah is the Messi of Africa and of course he has the skills to play for the best teams in the world," the Bayern chief told ON Time Sports per Goal.
"What he [Salah] has achieved can be compared to what Messi and [Cristiano] Ronaldo did with Barcelona and Real Madrid.
"At the moment we don't plan on signing Salah, but certainly it would be an honour to have him."
While Salah is still regarded as one of the Premier League's top wingers, it has been a tough season for Liverpool.
Jurgen Klopp's side don't look likely to retain their title and sit ten points behind league leaders Manchester City.
It comes off the back of City dismantling Liverpool 4-1 on Sunday afternoon and many have speculated if the club have reached the end of their cycle.
"We spoke before the game about that they are making a lot of excuses, but to me, they've been bad champions," Keane vented.
"I don't mean today, you can lose a game of football, but I can't figure this group out. Even in the game against Brighton, Brighton were comfortable against them...
"I think we've all believed the hype over the last year or two. We spoke about there being some sort of drop off, but they [the players] are playing for Liverpool.
"It's as if they won the league last year and got a bit carried away, and all believed their own hype that they were going to beat teams. But in my mindset when you've won a league title, the next challenge was always, can we do it again?
"I never got the impression from this group, from their interviews, even from their manager last year when they won it, saying what's the next step for Liverpool.
"I think they've been bad champions. We're talking about Liverpool, people keep telling me Liverpool are a great club and a huge club.
"Perform like champions, you're Liverpool Football Club. If you keep performing like that, it's going to be another 30 years until you win the title, trust me."
Featured Image Credit: PA Images
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