McClaren is reportedly urging Nketiah to pledge his allegiance to the Reggae Boyz.
Nketiah has one cap with England - which was earned in a friendly against Australia. As such, he can still play for Jamaica.
The striker left Arsenal for Palace on Friday for a fee of £25m rising to £30m in bonuses.
McClaren is also keen to bring Marseille forward Mason Greenwood into the fold.