Mahrez was linked with a move to Arsenal last summer after firing Leicester to the Premier League title – scoring 18 goals along the way.
The Algeria international ultimately opted to stay with the Foxes but, after struggling for form, now wants to quit the King Power Stadium.
Mahrez told the club of his intentions to leave earlier this week with Barcelona and Tottenham being backed to make a move for him.
Arsenal's interest could be rekindled, however, with Wenger refusing to rule out a move.
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Arsene Wenger has refused to rule out Arsenal signing Leicester star Riyad Mahrez
I like the player…it could happen
Arsenal boss Arsene Wenger on a bid for Leicester star Riyad Mahrez
Though the Frenchman has insisted the Gunners are yet to bid for the 26-year-old, he was coy when talking about whether he would attempt to bring Mahrez to the Emirates.
"We have not made a bid for him but personally I like the player, yes," Wenger told BeIN SPORTS.
"I think he had a huge impact at Leicester when they won the championship like everybody else at Leicester.
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"It's been a different season this year but it doesn't take anything away from his qualities.
Arsene Wenger is set to bolster Arsenal's squad this transfer window
"Have we made a bid for him? No. Not yet. Not yet means it could happen, it could not happen."
Arsenal are set to embark on an overhaul of their squad after finishing outside of the Champions League positions for the first time in 21 years.
As well as Mahrez, Monaco's Kylian Mbappe and Lyon's Alexandre Lacazette are two players on their radar.
However, Arsenal remain in a battle to keep hold of Alexis Sanchez, who reports claim is edging closer towards a move to Bundesliga champions Bayern Munich.