According to British media reports, including the PA news agency, the deal could include a further 11 million euros based on bonuses.
City manager Pep Guardiola said recently that Sane had rejected offers of a new contract and wanted to leave.
The 24-year-old Germany winger joined City from Schalke in 2016.
Sane only made his return to action last week after recovering from knee ligament damage sustained in the Community Shield in August.
While the Bundesliga campaign ended last weekend with Bayern defending the title, the Premier League runs until the end of July after being suspended