According to Sky Sports, the Hammers are interested in bringing in the free agent.
The former Manchester United left-back has been without a club since he was released by Marseille.
The club parted ways with the 36-year-old after Evra kicked a Marseille fan who he claimed was abusing him.
UEFA handed Evra a ban that runs until June 2018.
He made over 350 appearances for the Red Devils.