The German giants have made no secret of their desire to land the winger, whom they are believed to have come close to signing last summer.
Sane has not featured for City since August due to a knee injury, but Munich-based outlet TZ claims that Bayern are still desperate to bring him in ahead of next season.
However, the Citizens' valuation remains out of their reach so they apparently intend to use French defender Hernandez as a makeweight.
Hernandez, capable of playing at centre-back or left-back, arrived at Bayern from Atletico Madrid in a £71m transfer last year but has also struggled with injuries in 2019-20.
A separate report indicates that Sane is willing to take a pay cut in order to force through a move to the Allianz Arena. body check tags ::