Despite recently lifting the Bundesliga title for the seventh consecutive season, Die Roten are set for a major overhaul of their squad this summer and have reportedly made the City star their number one target.
With club stalwarts Arjen Robben and Franck Ribery both leaving Bavaria at the end of this campaign, Bayern are in need of some new faces in the wide positions and Sane is seen as the perfect addition to their squad.
Hoeness has now revealed the German champions are seeking a deal for the 23-year-old, who has struggled for game-time under City boss Pep Guardiola this season, completing the 90 minutes on just 16 occasions throughout the campaign.
The 67-year-old told German news outlet Suddeutsche Zeitung: "We are dealing with this player."
It is not yet known how much Bayern would have to pay to secure Sanes services although it is expected to be close to the club-record £68m they spent on Atletico Madrid defender Lucas Hernandez, who will join the club this summer.
The German side had previously been chasing Chelsea winger Callum Hudson-Odoi, making a £35m bid for the England international in January, however the players recent long-term achilles injury means they have now switched their attention to Sane.
The Germany international has seen himself ousted from the Sky Blues line-up for the majority of this season, with Guardiola preferring to play Bernardo Silva and Raheem Sterling in the wide areas.
That has led to Sane starting just 21 games in the Premier League during this campaign, although he still managed to get 10 goals and 10 assists in the top flight.