Alvarez joined the Hammers last summer from Ajax for a reported £34m and has since become a fans' favourite at the London Stadium.
The 26-year-old made a total of 42 appearances for West Ham across all tournaments last season, including 28 Premier League starts and six more in the Europa League.
Alvarez still has four years remaining on his Hammers contract and he is expected to be a key figure in the first-team plans of new manager Julen Lopetegui going forward.
However, speculation over Alvarez's future has surfaced in recent weeks amid interest from a few of Europe's elite clubs, including Man United.
Man Utd step up Alvarez pursuit amid Casemiro uncertainty
According to Sky Deutschland journalist Florian Plettenberg, Man United made an enquiry for Alvarez in the last few days and have 'gathered information about the figures' required for a proposed transfer.
Plettenberg claims that Red Devils manager Erik ten Hag has a high opinion of Alvarez and although West Ham are reluctant to part ways with the Mexico international this summer, he is not deemed 'unsellable'.
As things stand, West Ham are yet to receive any cash offers for Alvarez, who is valued between €60m (£50.7m) and €80m (£67.6m).
Man United's interest in Alvarez comes at a time when midfielder Casemiro is believed to be facing an uncertain future at Old Trafford.
A recent report claims that the Red Devils are 'almost sure' that Saudi Arabia-linked Casemiro will leave the club this summer and have identified Alvarez as a potential replacement.
Alvarez coy on West Ham future
It remains unknown as to whether Alvarez would be interested in joining Man United, but the midfielder is currently focused on representing Mexico at the 2024 Copa America.
Speaking to reporters, as quoted by the Metro, about his club future ahead of Mexico's Copa America opener on Saturday, Alvarez said: 'I can only tell you that I'm focused on what I have to do.
"I know that the Copa America is a very important tournament where the eyes of the world are basically here. Later there will be time to see what there is or what there isn't."
Alvarez is not the only midfielder on Man United's radar, as they are also believed to hold a strong interest in 19-year-old Joao Neves, who has reportedly turned down a contract offer from current club Benfica.
Ten Hag stated earlier this month that he wants to bring in a new central midfielder as well as a new centre-back and striker during this summer's transfer window.