The midfielder played another big part in Lyon's campaign which finished none too successfully with the club only able to secure 5th place, meaning that they will miss out on the all important European football.
The four time French international is now linked with a move to Roma with the Newcastle target possibly tempted by the prospect of a Champions League team after the Italian club finished second behind Juventus.
The attacking midfielder would be a valuable addition to the squad to support Miralem Pjanic who throughout the season has had no back-up to fill his role from time to time.
It is believed that with Lyon seemingly selling all of their valuable assets to balance the books, Grenier could be purchased for a fee of around 9-10 million euros.
With another 41 appearances under his belt this season, Grenier also added seven goals and eight assists to his name as well.