The Premier League outfit are said to be keen on bringing the 23-year-old Frenchman to St James' Park as a replacement for the departing Yohan Cabaye, who looks likely to join Paris Saint-Germain this month.
"I have learned that Newcastle are tracking me, but I still have targets with Lyon," Chronicle Live quotes Grenier as saying.
"If one day the time comes when I have to go, I will. The main thing will always to be to move forward. When you know where you want to go, you must establish it and achieve it."
Grenier has been previously linked with a move to Arsenal.