Eagles boss Roy Hodgson is keen on further upgrading his forward line after landing Michy Batshuayi on loan from Chelsea.
Benrahma, who plays for Championship side Brentford, has been among Hodgson’s primary targets in the current transfer window.
And Crystal Palace have stepped up their interest in the player.
However, the Londoners may need to spend top dollar to secure Benrahma’s signature with Brentford valuing the player close to the £20m mark.
Hodgson’s side will be hoping to land Benrahma after missing out on the signing of Liverpool hitman Rhian Brewster, who is edging closer to a move to Sheffield United.
The Algerian scored two hat-tricks and 17 goals in the Championship last season and it remains to be seen if his immediate future lies in the Premier League, with the transfer window slamming shut on Monday.
Nonetheless, Benrahma can still complete a potential move to the top flight, during an additional window for EFL transfers, which closes on 16th October.
