Mane joined the perennial Bundesliga winners from Liverpool for around £35m last summer after a successful six-year spell at Anfield.
However, the 31-year-old failed to make the desired impact in his debut season, scoring just seven goals in 25 Bundesliga appearances.
Mane's 2022-23 season was marred by his dressing room bust-up with teammate Leroy Sane after a Champions League knockout clash with Manchester City in April, with the Senegal international suspended and fines £250,000 for punching the German in the face.
Head coach Thomas Tuchel, who succeeded Julian Nagelsmann in March, recently acknowledged that Mane endured an underwhelming debut season at the Allianz Arena, telling Sport1: "He fell short of expectations.
"The competitive situation is extremely high, the starting position is not easy for him. The player knows that too, he knows my opinion and the opinion of the club."
Mane still has two years remaining on his contract at the Allianz Arena, but it is understood that Bayern are prepared to part ways with the forward after just 12 months.
A recent report claims that Mane is one of six first-team players who has been placed on the transfer list by Bayern, who are hoping to raise funds for their pursuit of top summer target Harry Kane.
Bayern's No.17 has recently attracted interest from the riches of Saudi Arabia, with Al-Nassr and Al-Ahli - two of four clubs that were taken over by Saudi Arabia's Public Investment Fund last month - said to be exploring a possible summer swoop.
According to Sky Deutschland, Bayern had initially quoted around £17m for Mane, but they are now asking for a figure closer to £27m plus bonus payments.
The report adds that representatives from both Al-Nassr and Al-Ahli have already made contact with Mane's entourage and will battle it out for his signature.
Al-Nassr are currently under a transfer embargo after failing to pay bonuses of around £400,000 to Leicester City for the transfer of Ahmed Musa in 2018, but FIFA will lift the suspension once the Saudi club pay the agreed settlement.
It remains to be seen whether Mane is interested in a move to Saudi Arabia, but he could follow in the footsteps of Senegal teammates Edouard Mendy and Kalidou Koulibaly, who have both left Chelsea to join Al-Ahli and Al-Hilal respectively.
Mane is currently training with his Bayern teammates and he is believed to be keen to travel with the first-team squad on their pre-season tour of Asia, which includes fixtures against former club Liverpool and treble winners Man City.
Mane is not the only Bayern player to have been linked with a summer exit, as the German giants are reportedly willing to entertain offers for midfielder Leon Goretzka, who is attracting interest from both West Ham United and Manchester United.