The America defender is currently on Mexico duty at the CONCACAF Gold Cup.
According to Futbol Total, Alvarez was first courted by Ajax, but has now attracted serious interest from the Premier League.
They claim Wolves were frontrunners to secure the 21-year-old, who would link up with compatriot Raul Jimenez if he were to make the move.
However, it's understood that West Ham have now made a formal bid for the player.
Alvarez is thought to be valued at £12 million by America.
The centre-back reportedly likes the idea of playing in the Premier League as he sees it as the most competitive league in the world.
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