Alvarez has been on West Ham’s radar since the end of last season and was one of their primary midfield targets.
However, the Hammers backed out of the race to sign him earlier in the summer when it seemed he was close to joining Borussia Dortmund.
But the move to Dortmund has collapsed and West Ham have rekindled their interest in signing the Mexican midfielder.
They have re-established contact with the Dutch champions to discuss a deal to sign the midfielder in the ongoing transfer window.
An offer has not been made yet but the Hammers are now expected to put in a bid for him soon.
Ajax want a fee of somewhere around £35m to £40m for the 25-year-old Mexico international.
Alvarez was a constant presence in the Ajax midfield last season, stacking up 44 appearances in all competitions.
David Moyes wants to sign two midfielders to replace Arsenal-bound Declan Rice and the Ajax star is one of his top targets.