The Daily Express says Grenier recently hinted that he could leave Lyon this summer
On international duty for France, he said: "We will see about my future after the internationals, during my vacation."
Wenger has compared him to former Gunners star Samir Nasri.
"We are following him," Wenger revealed last month. "His intelligence of play pleases me. He has interesting qualities. He reminds me of Nasri."