The Algerian international made it clear at the end of last season that he wants to leave the Foxes, but so far the club have not accepted any bids.
Roma were thought to be the frontrunners for Mahrez's signature, but the Italian outfit withdrew their interest earlier this month after having a £30m bid turned down.
Petit believes that the winger, who scored 17 goals and produced 11 assists in Leicester's Premier League-winning season, fits the bill at Arsenal.
"He knows the Premier League by heart, and has an incredible impact in it, "Petit told SFR Sport. "He's the kind of player sorely lacking for Arsenal down the right.
"I say stop focusing on the problems at the back. I'm among those who think the further away the ball is from your goal, the less chance you have of conceding a goal. And the more players you have who are capable of holding on to the ball. How many players are there in world football of that profile?
"If I were a coach I'd love to have dribblers in my team - quick, technically good, capable of saying [to a defender], "I'm going to humiliate you with two feints, two step-overs'."