The reported Arsenal target has scored 10 Ligue 1 goals from 15 starts this season.
The Rennes forward, who has netted 10 times in 15 Ligue 1 starts this season, has emerged as one of the hottest properties in European football and has been linked with a summer move away.
The £27m-rated starlet reportedly courted interest from Arsenal (The Mirror) earlier this month.
According to the report, Dembele will sign for the Bavarians but return to Rennes for a season-long loan during the 2016-17 campaign.
Along with boasting a very decent goals record in his breakthrough season, Dembele has also bagged five assists from his 15 Ligue 1 starts and, if true, Bayern appear to have signed quite a talent.
Arsenal boss Arsene Wenger might well be in the market for another striking option this summer as Olivier Giroud blows hot and cold, while Danny Welbeck is untested at the Emirates Stadium over a nine-month season.