The 28-year-old's contract at Allianz Arena is due to expire in June 2025, and he has not yet managed to come to an agreement with the Bundesliga giants over an extension, with a departure next summer on a free transfer certainly possible.
A number of clubs, including Arsenal, Chelsea, Liverpool and Newcastle United, have been credited with an interest in Sane, but according to Germain journalist Florian Plettenberg, Man United are also in the mix.
Discussions between Sane and Bayern over a new contract are believed to have stalled, and as it stands, he would be free to enter into negotiations with foreign clubs over a pre-contract at the start of 2025.
Sane has found it difficult to break into Bayern's first XI in the early stages of the campaign, but he has still contributed three goals in 10 appearances despite finding it difficult to secure starts.
Man United 'interested in potential free agent Sane'
The forward's only start of the season came against Mainz 05 in the German Cup at the end of October, with his four Champions League appearances and five outings in Germany's top flight all coming off the bench.
Sane is believed to be ready to seek pastures new next year, and he would certainly be one of the most attractive free agents on the market considering his age and what he has achieved in the game.
The forward has scored scoring 51 goals and registered 50 assists in 185 appearances for Bayern in all competitions, winning three Bundesliga titles in the process, while he has experience of playing in the Premier League.
Sane made 135 appearances for Man City ahead of his return to Germany, scoring 39 goals and registering 43 assists, winning two Premier League titles, one FA Cup and three League Cups in the process.
Would Sane be a good signing for Man United?
Sane largely operates as a right-sided attacker, which is a position that continues to prove problematic for Man United.
Neither Antony nor Amad Diallo have convinced in that area, while Alejandro Garnacho and Marcus Rashford both play their best football down the left, so there is a clear need for a specialist in that position.
Much will depend on the plans of incoming head coach Ruben Amorim, though, and whether he decides to implement his preferred 3-4-3 system, with Sane potentially being asked to operate in a more central area.
Sane hit double figures in terms of goals in two of his three full seasons in the Premier League, and he could now potentially be given the chance to reignite his career back in a familiar city.