Gomis has long been on Newcastle's radar, and they agreed terms with Lyon earlier this month - only for the deal to stall.
Newcastle initially pulled away from the transfer two weeks ago, and Lyon even opened talks over a new deal for the 28-year-old France international, who has rejected numerous offer to leave the Ligue 1 giants over the past 12 months.
But now Newcastle have decided to return to the deal and have opened talks with Gomis and his representatives once again.
It is understood Gomis's camp is willing to drop their own demands, which has given Newcastle the belief that a deal can now be struck before Monday's deadline.
Newcastle have only brought in Loic Remy - on loan - and French youngster Olivier Kemen so far this summer.