Sky Germany reports that Stefan Ortega is the favorite to become Bayern's new goalkeeper, with David De Gea seen as an alternative.
According to Sky Germany, Bayern coach Thomas Tuchel has held a phone call with the Manchester City goalkeeper, who is said to be seriously considering a move.
However, there is also the question of whether Manchester City would be willing to let Ortega go, with their manager Pep Guardiola recently admitting that "it would be a problem to lose him".
Should Bayern fail in their bid to sign Ortega, they could move for David De Gea instead.
The 32-year-old, who is a free agent after leaving Manchester United, has given the green light for a move to Bayern should the opportunity arise, Sky Germany reports.
Yassine Bounou, who has also been linked with Bayern, is said to be close to a move to Saudi Arabia's Al Hilal.
With Manuel Neuer still working on his comeback from injury, Sven Ulreich is currently the only senior goalkeeper in Bayern's squad.