The 25-year-old's current deal at the Allianz Arena is due to expire in June 2023, and the German champions are allegedly finding it difficult to agree fresh terms with the attacker.
Coman has again been a regular for Bayern during the 2021-22 campaign, making 10 appearances in all competitions, providing two goals and one assist in the process.
However, according to Defensa Central, there is also genuine interest from Real Madrid, who are keeping a close eye on the developments in Germany.
The report claims that Carlo Ancelotti's side would be prepared to offer up to €35m (£30m) for his services during next summer's transfer window.
Coman has won league titles in France, Italy and Germany during a glittering career to date, turning out for Paris Saint-Germain and Juventus before making the move to Bayern.