The 23-year-old has been linked with a switch to St James' Park for some time, and talk has intensified since it emerged that Newcastle's Yohan Cabaye is set to join Paris Saint-Germain.
France international Grenier, however, insists he is in no rush to leave the Stade de Gerland, where he came through the youth system.
"I have learned that Newcastle are tracking me, but I still have targets with Lyon," the midfielder is quoted as saying by Chronicle Live.
However, Grenier went on to indicate that he does not see his long-term future being at Lyon.
"If one day ... the time comes that I have to go, I will," he added.
"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, who has three France caps to his name, has made 20 Ligue 1 appearances for Lyon this season, scoring four goals.
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