Remy is expected to leave Chelsea following the singing of Radamel Falcao from Monaco.
The report states that The 28-year-old is keen to remain in London and play for Palace.
The Black Eagles are in the market for a striker after Chinese giants Shanghai Shenhua snapped up Demba Ba for €14 million.
Beşiktaş have made it clear that they will sign a replacement striker and have also been linked with Hull City forward Dame N’Doye. The Black Eagles have also been closely linked with a move for FIorentina’s striker Mario Gomez.
Remy played under Pardew for two seasons at Newcastle where Remy scored 14 goals in 26 games.
Pardew has been busy in the transfer market this summer having signed Yohan Cabaye from PSG for £10 million.