The Magpies were heavily linked with the powerful forward over the summer, but failed to secure a deal after being in talks with his representatives.
Despite this, they have since remained keen on Gomis, with rumours of a move this month having circulated for some time.
But, they may have to push ahead their plans for a deal with Inter circling.
The Serie A side have made the forward one of their top targets for the coming week, and are keen to push through a deal.
Gomis is set to be a free agent in the summer, and Newcastle are rumoured to be now looking into waiting until then to snap him up for free.
However, the Milan giants are plotting a cut-price swoop in the coming days.
Gomis has netted an impressive seven goals in 16 outings for Lyon this term, and is an outsider for Les Bleus’ World Cup squad.