The Algerian was the PFA Player of the Year in the 2015/16 season when he scored 17 goals in Leicester's title winning campaign but managed only six last year, which has seen his stock dip significantly.
The Daily Mail reports that Mahrez has already put in a transfer request but his future is in limbo as both clubs are struggling to agree a fee. The 26-year-old has spoken to Leicester, who have assured him that he will be allowed to leave this summer after being asked to stay put last season.
Wenger has already stressed that a dip in Mahrez's form last season should not take "anything away from his qualities".
The Gunners' manager publicly expressed his admiration for the former Le Havre man but confirmed that no bids were made for the player, while talking to beIN Sports in June.
"We have not made a bid for him but personally I like the player, yes. I think he had a huge impact at Leicester when they won the championship, like everybody else," Wenger told beIN Sports, as quoted by ESPN.
"It's been a different season this year but it doesn't take anything away from his qualities. Have we made a bid for him? No. Not yet. Not yet means it could happen, it could not happen.''
The Gunners are also pursuing a deal for Thomas Lemar but have received a major setback, with Monaco demanding £80m ($103m) for the 21-year-old.
However, Arsenal have come back with an improved bid and hope to get the transfer over the line as soon as possible.
The forward has scored 14 goals in the recently concluded campaign and has been among the standout players for the Ligue 1 champions.
Lemar has two years left on his current contract and has refused to sign an extension with Monaco, indicating that he would be open to a move if the right offer arrives.
The young forward is known for his versatility and can play as a winger or behind the striker. With his best years ahead of him, he will be a massive asset for the north London club, should they be able to complete a deal for the player.