Having lost key playmaker Yohan Cabaye in a £23m transfer to Paris St Germain earlier in the week, Magpies manager Alan Pardew is keen to bolster his midfield options ahead of Friday's deadline.
But Lyon have turned down what Pardew called a "substantial" bid at an earlier press conference, during which he seemed confident of bringing the 23-year-old to St James' Park.
Pardew had said: "I don't know. We have two days left and we will have to wait and see. I'm obviously hopeful.
"He (Grenier) has tremendous creative technical ability and he's a player that Newcastle fans would love to see at the football club.
"But he's still not our player, so until he is... I will wax lyrical about him then."
One man already signed up at Newcastle ahead of the deadline is striker Luuk de Jong, a loan acquisition from Borussia Monchengladbach who goes straight into the squad for Saturday's derby clash with Sunderland.
Pardew said of the Dutchman: "I'm pleased in so much that he's a player we have had our eye on for a while.
"He was someone we couldn't quite reach in his last transfer move in terms of the finance, but that hasn't worked out as perfectly as perhaps they both hoped, the team and Luuk, and he's ended up here.
"But he has done well today and we are looking forward to his inclusion in the squad.
"He's a big presence of a player, he's a goalscorer and if there's a criticism you would aim at us, maybe we could do with scoring a few more goals."