The Frenchman only joined the Swans from Lyon on a free transfer over the summer, but has been used infrequently by manager Garry Monk.
Of Gomis’ 15 outings – in which time he’s netted twice – the 29-year-old has started only four times, which is rumoured to be a great source of frustration for him.
This has alerted Palace chief Neil Warnock, who is looking to add more physicality to his forward line in January.
The Eagles gaffer is ready to present the former Les Bleus star with regular playing time, and is hopeful that it will be enough to lure him across from South Wales.
Palace have promised Warnock funds for next month, which should allow him to trigger Gomis’ release clause, rendering Swansea powerless in the situation.
The Swans are far from keen to lose their man, with star striker Wilfried Bony set to be absent for much of January due to the African Cup of Nations – where he’s set to represent Cote d’Ivoire.