The capital club are pushing to give manager Diego Simeone a more productive front line.
While some forwards may leave, such as Joao Felix, Alvarez is one they very much want to sign.
Per TyC Sports, he would then get the chance to play next to Argentina colleague Rodrigo De Paul.
Alvarez has been happy at City in the past, but may want to find a new challenge.
He is very much behind Erling Haaland in the pecking order to start games when all players are fit.