The France international midfielder admits being tempted by offers in the summer but eventually signed a new contract instead and is happy to stay at the Ligue 1 club
Gunners boss Arsene Wenger confirmed his interest in the midfielder in the close-season but the 22-year-old elected to instead sign a new contract with the French side.
The France international has scored three goals in 18 appearances for Les Gones this season but, despite his club's disappointing mid-table position in Ligue 1, has no intention of moving on yet.
"A departure last summer? I was not against that at first but, finally, I took my time on thinking what was best for me," Grenier told Telefoot.
"Now I want to do better and better with OL. It has been a little complicated for me lately but I will not let go. This winter the club has not decided to sell me.
"In football anything can happen but it is not relevant today. I decided to continue with OL; they have helped me a lot since I was little. At the moment, I do not see myself leaving."