Chelsea and PSG are among the clubs interested in signing the £70m striker.
Alvarez’s decision to reject the contract indicates his desire to move on from Manchester City.
The striker’s potential departure has attracted attention from top clubs in Europe.
Alvarez turned down a new contract at Manchester City and is looking for a new challenge.
Chelsea and Paris Saint-Germain are interested in him but must pay at least £70million to sign him.
Losing Alvarez would be a big blow for City as he has played an important role under Pep Guardiola.
Alvarez has already won the World Cup, Copa America, Premier League, Champions League, FA Cup, and League Cup.
He is tied to his contract until 2028 and will report for pre-season with his team-mates.