The 20-year-old has scored 33 goals and nine assists in 70 games in all competitions for his Uruguayan club, including 23 goals and five assists in 40 games this season.
Real Madrid became earlier this year ascribed an interest in the attacker, although Los Blancos are interested in signing him for their Castilla team in order to be promoted to the first team.
According to Mundo Deportivo, there is also real interest from Barcelona, according to Mundo Deportivo of their financial troubles looking for cheap signings in 2022.
The report claims a € 12 million (£ 10.2 million) offer is likely to be accepted by Uruguayan champions Penarol.
Alvarez, who only scored one goal in four games for Uruguay, has a contract with his current club until June 2024.
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