Patrice Evra has arrived at West Ham's training ground ahead of a proposed free transfer, Sky Sports have reported.
The former Manchester United full-back was seen at the club's Rush Green training complex on Wednesday morning and is expected to sign a deal until the end of the season.
Everton are also reportedly interested in the Frenchman, but he is said to prefer a move to London.
Evra has not played since he was dismissed by Ligue 1 club Marseille in November after an altercation with a fan.
The 36-year-old kicked out at the supporter who he claimed had abused him before a Europa League defeat against Vitoria, and was banned by UEFA following the incident.
Evra was charged under article 15 of UEFA's disciplinary regulations, banning him from their competitions until June 2018.
That does not prevent the defender from playing in any domestic competitions, so he is eligible for the Premier League.
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Evra joined Marseille in January last year on a free transfer after a two-and-a-half year spell with Serie A champions Juventus.
He had previously spent eight years at Old Trafford, winning the Champions League and five Premier League titles.
Evra made 379 appearances and scored three goals as an integral part of his side's back four. His final campaign with United saw David Moyes take over from Sir Alex Ferguson, and Evra could now be set to join up with the former Scotsman again.