According to The Mirror, Palace are keen on the defensive midfielder, as they look to bolster their midfield options.
Arsenal are ready to let Coquelin leave this month after he lost his place in Arsene Wenger’s team.
Coquelin wants regular game time, which Wenger can no longer guarantee, leaving him with no choice but to seek a way out.
Palace are looking to offer him an escape route, to Selhurst Park, as Roy Hodgson looks to move in.
The 26-year-old was omitted from the matchday squad for Arsenal on Sunday as they fell to a 4-2 defeat at the hands of Championship side Nottingham Forest.
The report claims Arsenal want around £10m for Coquelin, although it is not stated whether Palace are ready to match that fee at this moment in time during the window.