Remy made the move to Stamford Bridge in 2014 from Queens Park Rangers after a successful loan spell at Newcastle United and much was expected from the striker due to his exploits at the time.
However, the France international has been plagued by injuries during his time with the Blues and, when fit, his performances have not been enough to dislodge Diego Costa from the central striking role.
The 30-year-old joined Crystal Palace on a year-long loan last summer but a knee injury resulted in just five Premier League appearances being made, with just one of those starts.
Remy is surplus to requirements at Chelsea and the reigning league champions are ready to accept a cut-price deal to get the striker off the wage bill, and make way for a new arrival.
French outfit Rennes, who finished ninth in Ligue 1 last season, are believed to be showing a keen interest and they could wrap up a deal for the Frenchman in the coming weeks.
Remy has previously enjoyed success in his homeland, with 54 league goals being scored in five years at Nice and Marseille respectively.