Earlier this month, City manager Pep Guardiola revealed the 24-year-old attacker refused to agree a new deal at the Premier League club which only had 12 months left to run.
And German news outlet BILD say a five-year deal has been agreed for Sané to return to the Bundesliga ahead of the start of the 2020/21 season, but paperwork has yet to be signed.
The Independent claim the deal will cost Bayern Munich up to £55million, with £44.7million to be given to City up front with £11million in add-ons
City have also inserted a 10 per cent sell-on clause into the deal, meaning they will earn a portion from any money Bayern receive should they decide to move Sane on in the future.
A move to Bayern Munich would end four-year spell at the Etihad Stadium, which has seen the German winger win two Premier League titles, two EFL Cups and last season’s FA Cup.
Overall, the winger has made 135 appearances for Guardiola’s squad, scoring 39 goals.