The Blues have scored 35 goals in all competitions this season, with only five of those being scored between new strikers Joao Pedro, Marc Guiu and Liam Delap, who is yet to get off the mark.
According to Fichajes.net, the Premier League side have identified Alvarez as a key summer signing to bolster their attack and are reportedly considering making a 150 million Euro offer.
However, they could face a battle from Barcelona and Paris Saint-Germain who are also said to be monitoring his situation with Los Colchoneros.
The 25-year-old World Cup winner joined Atletico in a surprise move from Manchester City following the conclusion of the 2023/24 season.
He has impressed since joining the La Liga club, scoring 38 goals and providing 12 assists under the guidance of Diego Simeone.
The Argentina forward was set to get his 50th cap in the international friendly against Angola on Friday but will miss out alongside teammates Guiliano Simeone and Nahuel Molina.
The trio reportedly failed to complete yellow fever vaccination requirements needed to enter Angola and have remained in Spain.
