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!
Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?