The 26-year-old winger has enjoyed another stellar season with the German champions during the 2021-22 campaign, contributing 17 goals and 10 assists in 44 appearances across all competitions.
Gnabry possesses a contract until the end of the 2022-23 campaign, though, and there has been a number of speculation surrounding his future over the last few weeks.
A recent report suggested that the Germany international had turned down the chance to sign a lucrative deal with the Bavarians.
Arsenal, Tottenham Hotspur, Liverpool and Juventus have previously been credited with an interest, but according to Fichajes, Los Blancos are currently in pole position for the attacker’s services.
The Bundesliga giants are not in a strong position to demand a high fee for Gnabry and would run the risk of losing him on a free next summer.