The Magpies star looks set to join PSG after the Ligue 1 champions agreed a fee – rumoured to be in the region of £20m – for his services.
With the ex-Lillie man so influential in Alan Pardew’s side a replacement will be needed, and Grenier is seen as the ideal man to fill the void.
The 23-year-old has been earning rave reviews for his domestic displays this term, and has even earned recognition on the international stage with three caps to his name
Arsenal have also been linked with his signature, but Newcastle are hoping that a £10m swoop before the end of the week will be enough to beat the Premier League leaders, who are said to be closely pursuing Julian Draxler.
Remy Cabella is also a target, but negotiations with Montpellier are believed to have stalled.
If Grenier completed the move he will join a Newcastle squad littered with Frenchman, with the likes of Loic Remy, Mathieu Debuchy and Moussa Sissoko currently plying their trade on Tyneside.