Norwich City want to bolster their forward ranks in January.
Norwich had been tracking Gayle last summer, but they were unable to force through a move before deadline day.
The Canaries are now set to re-ignite their interest in the 25-year-old, after selling Lewis Grabban to Bournemouth.
Norwich received £8 million for Grabban, according to the Mirror, and they plan to re-invest these funds on Gayle.
The former Peterborough United man has finished as Palace’s top scorer in the last two seasons, but he has dropped down the pecking order at Selhurst Park recently.
Gayle is now Palace’s second choice striker, following the arrival of Connor Wickham from Sunderland.
Gayle has still managed to notch four goals this term, but Alan Pardew appears to have reservations over using him regularly.
Palace are reportedly willing to sell Gayle, but they will not sanction any loan moves.