The Eagles are desperate to bolster their attacking options this summer and failed with a £30m bid for Liverpool's Christian Benteke on Tuesday.
Palace are expected to come back with another offer for the Belgian, but manager Alan Pardew is keen to sign two strikers before the transfer window.
And, according to L'Equipe, Remy is the player he has identified to bring in alongside Benteke.
The Frenchman is ready to leave Stamford Bridge in search of first-team football and Everton have already expressed an interest.
But the opportunity for Remy to stay in London and work with Pardew again - who he played under at Newcastle - is likely to give Palace the edge.