Alvarez is the man of the moment for River Plate, with him scoring a brace to help them get a 2-1 win against their arch rivals Boca Juniors in the Superclasico.
According to a report from Calciomercato.com, the River Plate forward is at the top of the wish list for several clubs, one of which being Milan.
The 21-year-old's two goals against Boca Juniors has allowed River to go to the top of the table, continuing his excellent start to the season after he won the Copa America with Argentina over the summer.
In just 11 games, Alvarez has already got seven goals and four assists, with the Rossoneri reportedly being one of the most active clubs when it comes to their interest in him.
Milan believe that he would offer the club similar qualities to what Ante Rebic has, with both of the players being very hard working and aggressive forwards.
While Milan wanted to sign him last year, River wanted the full €25 million for his release clause, which led to the deal being halted.
However, Alvarez's contract is set to expire in December 2022, and so there is a high possibility that the Argentine club will make the forward available for a cheaper price.