The former Schalke winger had been linked with a return to Germany after starting just 21 Premier League games under Pep Guardiola last season.
But Sky Sports reports that the Bundesliga champions have accepted that they are unlikely to strike a deal for the Germany international this summer.
Sané is set to travel to Asia with Manchester City's squad on Monday for their pre-season tour, and it is said that the Citizens are confident he wants to stay.
Bayern had made the 23-year-old their top target but needed the forward to request an exit, which he hasn’t done as he feels his future lies at the Etihad Stadium.
The German giants would also have to meet City’s demands of more than £100 million, and as such are yet to make a bid and have turned their attention elsewhere.
Bayern are understood to have revived their interest in Chelsea’s Callum Hudson-Odoi as well as Arsenal target Yannick Carrasco, who is currently on the books of Chinese Super League side Dalian Yifang.
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