The Olympique Lyonnais ace claimed in May that a decision had already been made following Arsenal interest but now says he will consider later
The 22-year-old claimed in May that he had already determined his next move but did not disclose whether he was staying with the French club or linking up with Arsene Wenger's side.
Grenier is currently on international duty with France and earned his first senior cap after coming off the bench in his nation's 1-0 defeat to Uruguay on Wednesday.
"I'm training here in Uruguay and Brazil. It feels good to be far from France right now because I've heard a lot of things about me lately," the midfielder told reporters.
"I can't give answers to everybody. I want to enjoy these 10 days of training. We will see about my future after the internationals, during my vacation."
Earlier in May, Wenger confirmed to French football programme Telefoot that his side were tracking Grenier and likened the midfielder to former Arsenal player Samir Nasri.