Magpies chiefs had been locked in talks with Lyon and Gomis over the past few weeks, and they were hopeful of pushing the deal through well before now.
However, with no signs of progress, Newcastle have now switched their attention to other targets, and it appears unlikely at this stage they will be back for Gomis. Meanwhile, their interest in Aston Villa's Darren Bent is also believed to have cooled.
Lyon chief Jean-Michel Aulas has now stated that there are no offers left on the table for Gomis, suggesting that indeed Newcastle have pulled out.
He told Lyon's website: "We have to be humble, I'm ready to make myself available to discuss the situation with Bafetimbi. I think we both need to swallow our pride, myself being the first.
"But there are no offers currently on the table.
"Bafetimbi needs to play football. I believe it would be a mistake to stay entrenched in our current positions. We have to work with his agent to find an amicable resolution that will see him happy to stay at Lyon."
Aulas is also ready to make peace with Yoann Gourcuff and offer him a new deal after reports claimed that Lyon were ready to loan him out.
"Yoann is part of Lyon team that will surprise a lot of people. L'OL has never thought about loaning Yoann Gourcuff paying half of his wages. It is amazing to hear such things," he said.
"I have initiated discussions with his agent to offer him a contract extension."
In their opening game of the season which they won 4-0 against Nice, Gourcuff scored and created two more.