Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
A bid from Newcastle for Lyon midfielder Grenier has remained on the table as the Magpies pursue a replacement for Yohan Cabaye, who joined Paris St Germain this week.
But agent Frederic Guerra has announced Grenier will stay with his French club.
He told French sport website Le 10 Sport: "It's not easy to say no to a big club like Newcastle, but with Clement we have finally decided to stay at Lyon.
"Six months out from the World Cup, is a hasty departure just days before the end of the transfer market a good option? It's not a certainty. Lyon are starting to find their true colours and Clement didn't want to leave the club during the season.
"The conditions of his departure weren't creating a favourable context for his development. Clement would be arriving at Newcastle not as Clement Grenier but as a replacement for Yohan Cabaye.
"I have the greatest respect for the quality of player that Cabaye is, deserving of everything that is said about him. However, as Clement Grenier's agent I am obliged to say: is Clement worth just half what Yohan Cabaye is?
"Above all the reasons which have led us to decline the offer from Newcastle, the conditions of the deal didn't seem fair to Clement."