The French side made an offer to take the Algerian on loan until the end of the season in a proposed deal that would have included an option to make the move permanent in the summer.
The Hammers are open to Benrahma’s departure this month but are thought to prefer a permanent sale as they look to bolster their own budget for attacking reinforcements.
Benrahma scored one of the most important goals in the club’s recent history in the Europa Conference League final triumph over Fiorentina in June but has slipped down the pecking order this term following the summer signing of Mohammed Kudus from Ajax.
The former Brentford man has made just five Premier League starts and is yet to find the net in 21 appearances across all competitions.
Despite uncertainty over his future, however, the 28-year-old was named in David Moyes’s starting lineup for Tuesday night’s FA Cup third round replay at Bristol City, after knocks for Pablo Fornals and Edson Alvarez added to the Scot’s mounting injury list.