The 24-year-old has been in stunning form for high-flying Leicester this season.
The Algeria international has bagged seven goals and managed six assists in 12 games for Claudio Ranieri's men.
And French news outlet Foot365 report that Wenger is readying a bid for the winger as he looks to add more depth to his injury ravaged squad.
Mahrez has also been heavily linked with a move to Manchester United, along with his teammate Jamie Vardy.
Despite the interest in his star players, Ranieri has urged Mahrez and Vardy to stick with the Foxes.
He said: "I think we are building a very good construction.
"I understand if somebody wants to go but I believe in the next year Leicester, slowly, slowly, can grow up and battle with the top.
"At moment we're very happy and also Jamie is happy with us and he can continue to show his strength with us. Jamie, Riyad, everyone.
"This is our project. I spoke to the owners not now, in July about it. People believe in me - I believe in me too."
