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.
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
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.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.