The German champions have made no secret of their interest in Sane, failing in their attempts to bring him to Munich last summer before deciding against a move in January due to his knee ligament injury.
However, Bayern are expected to revive their pursuit of the Germany international when the transfer reopens again, and Bild reports that manager Flick has been at the front of the charm offensive.
The report claims that Flick spent 30 minutes on the phone to Sane, although what the pair talked about is unknown.
The 24-year-old forward has not tasted first-team action since the Community Shield in August but was on the brink of a return from injury before the action was halted due to the coronavirus pandemic.
Sane's current deal at the Etihad Stadium expires next summer and Man City could be tempted to cash in on the attacker rather than risk losing him for free in 2021.