The Blues appear to be concentrating their efforts on signing Fiorentina winger Juan Cuadrado, but The Mirror suggest they've made a surprise swap bid with their Premier League rivals.
Summer signing Remy joined from QPR back in August in a deal believed to be worth around £10.5m, but has been a bit-part under Jose Mourinho this season.
With just one start and 188 minutes to his name as a Chelsea player, Remy is little more than an afterthought in attack with Mourinho preferring to use Diego Costa and Didier Drogba up front.
It's still something of a shock to see him offered up in a potential swap deal, especially for West Ham striker Valencia - who also only joined the Hammers last summer.
The Ecuador international was one of the stars of the World Cup, scoring all three of Ecuador's goal in Brazil as they crashed out in the group stage.
West Ham paid a reported £12m to bring the 25-year-old to East London from Mexican side Pachuca, and whilst he's only hit three goals, he's impressed with his electric pace in attack - a welcome addition from a supporters point of view, considering the over-reliance on Andy Carroll's aerial ability last season.
The Mirror report that whilst Remy has been offered to Sam Allardyce's men in a swap deal, West Ham are adamant that Valencia won't be leaving Upton Park as they push towards European qualification.
Valencia's versatility to play up front or out wide is key for Allardyce, and whilst Remy would be a good addition, it's unsurprising that West Ham want to keep hold of Valencia.
Here are some stats comparing Remy to Valencia - who would you rather have?
|Position||Team||Shots on Goal||Shots on Target||Goals||Appearances||Minutes Played|
|Enner Valencia||FW||West Ham||38||9||3||19||1,048|
|Loïc Remy||FW||Chelsea / QPR||14||6||2||11||366|