Bayern can offer around ?8million for the former Hamburg defender, 22, who City bought for ?12m last summer.
On the move: Bayern are looking to tie up a deal for the Manchester City defender
Boateng's most recent start for City came in late February, while he last made an appearance in a matchday squad two months ago.
German magazine Kicker reported on Monday that a four-year deal had been struck between Bayern and the player, with the matter of a fee proving to be the only stumbling block.
Bayern, who have already agreed to spend almost ?20m on Schalke goalkeeper Manuel Neuer, want to strike a deal for 'significantly less' than City paid.
?Bayern Munich close in on deal to land Manchester City defender BoatengMancini to battle board for cash as City boss plots Champions League successBayern eye return trip to Germany for Boateng alongside Adebayor Manchester City FC news, features and opinion
?Explore more:Places: Manchester, Munich
Source: Daily Mail
Source: Daily Mail