The Toon have spent big already in January, with the likes of Jonjo Shelvey and Andros Townsend contributing to nearly £30million in transfer fees since the turn of the year.
Crystal Palace and Michael Laudrup-managed Qatari side Lekhwiya SC were the two favourites with the bookies to sign Gomis earlier this month but now Newcastle are clear at the top of the list.
Swansea are close to sealing an £8million move for Chievo striker Alberto Paloschi and that would drop Gomis back down the pecking order.
After a strong start to the season, scoring four in four in the early stages, Gomis has since notched just twice in his last 19 appearances.
Palace were, and still are, keen on the forward but the signing of Emmanuel Adebayor means they may not make a move for him this month.