The former Sunderland star is available on a free transfer after ending his contract with Lyon during the summer.
Mensah impressed last season while on loan at Sunderland.
The 29-year-old is a free agent and is able to hold talks with any club despite the transfer window closing on Friday night.
The Daily Star reports that the Hammers are keen to agree a deal with the defender as soon as possible.
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Being an amiable guy is good for you and Jurgen Klopp is living proof.
Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.