Mahrez has asked to leave Leicester after his form deteriorated last season, following his stunning contribution to the Foxes’ Premier League title win 12 months earlier.
Leicester are unlikely to allow Mahrez to leave cheaply, despite the Algeria international netting just six Premier League goals last season.
But after penning a new two-year contract at the Emirates, Wenger is expected to have money at his disposal this summer and says a move for Mahrez is a possibility.
"We have not made a bid, but personally, I like the player, yes," Wenger told beIN Sports.
"I think he made a huge impact when they won the championship.
"Like at everybody else at Leicester, this season has been more challenging, but it doesn't take away from his qualities.
"Have we made a bid for him? No. Not yet. No, we have not. When I say 'not yet' it means it could happen. It might not happen."