The Palace frontman has become surplus to requirements at Selhurst Park.
The 24-year old has found himself slipping down the pecking order with the Eagles following the arrivals of Connor Wickham, Patrick Bamford and Bakary Sako, and will struggle for game time this season.
The report claims Norwich were close to securing the services of the nippy frontman on transfer deadline day before Alan Pardew pulled the plug on the deal at the last minute.
The Palace boss was happy to allow the striker to leave until summer signing Connor Wickham picked up a hamstring injury during deadline day training.
Canaries manager Alex Neil remains a fan and will return in January, with Palace likely to accept an offer barring any further injuries to their forwards.
Gayle has proven his abilities in the top flight and would be a shrewd acquisition for the newly-promoted club.
His lack of involvement at Selhurst Park is something of a surprise, given his goal return and experience in the Premier League trumps that of his striking competition.