Distin has been told that he can leave Goodison Park on a free transfer and the Hammers believe he could be a bargain buy.
The 37-year-old has been a regular in Everton's side for a number of seasons, but he has fallen out of contention this term and a change of environment may be needed.
Sam Allardyce is known to be targeting a centre-back before the transfer window closes, and Distin is apparently near the top of his wishlist.
What's the impact for West Ham?
Distin's age has been catching up with him this season, but he may be a decent option for West Ham as cover.
Although the Frenchman would be unlikely to break into their first-team, his knowledge and experience would make him a suitable covering option.
Distin is never likely to be a long-term solution, due to his age, but he could be invaluable to the side as they look to claim a European spot this campaign.