Mane joined the German champions last week in a £35m deal, signing a three-year contract.
In six years at Anfield, Mane helped Liverpool reach three UEFA Champions League finals, winning one, and his list of laurels also included the Premier League, FA Cup, UEFA Super Cup, FIFA Club World Cup and Carabao Cup.
He also scored 120 goals in 269 games for the Reds.
Despite his immense contributions for Liverpool, it was reported that Mane's wages was nothing to write home about, with the likes of Alex Oxlade-Chamberlain earning higher than him.
But Mane's PR agent Bacary Cisse maintains the former Southampton forward simply wanted a new challenge.
"Those are false rumours," Cisse told TV5Monde. "We didn't want to talk about that. A player of Sadio's calibre can't be earning the salary that people are speaking about. The numbers circulating are completely wrong.
"Sadio was already earning more than that when he joined Liverpool from Southampton. He extended his contract in 2018 and his salary was much higher than the numbers circulating in the media."
"He won everything with Liverpool and it was time to seek a new challenge elsewhere," Cisse added.
"Bayern's project was very attractive. Bayern came knocking. Sadio, his German agent Bjorn Bezemer and I had a discussion. Many other very big clubs, that I won't name, wanted Sadio, but when we saw Bayern's project we said, 'That's it, we have to go there'.
"The coach [ Julian Nagelsmann ] and the sporting director of Bayern [Hasan Salihamidzic] travelled personally to Liverpool, there was a very good meeting in Sadio's house and we discussed the contract."
