Arsene Wenger wants the Algerian, who starred for Leicester in their title win last season, to bolster his forward line which already includes Alexis Sanchez, Mesut Ozil, and Theo Walcott.
After Mahrez decided on a move to Emirates Stadium, the move could happen soon with a price around the €50m mark.
Arsenal's French coach Arsène Wenger looks on during the football match Lens Vs Arsenal on July 22 2016, at the Felix Bollaert stadium in Lens
Image credit: AFP
It will be a further blow to manager Claudio Ranieri after he already lost star midfielder N'Golo Kante for £30million to Chelsea.
The Italian had told Sky Sports earlier in the week: "It's over, the market is over here, Mahrez wants to stay."
However, it is understood the 25-year-old's agent met Arsene boss Arsene Wenger in Lens, where the Gunners were playing a pre-season friendly on Friday.
The deal could be announced in the next few days after Wenger said at a press conference that the club are still very "active" in the transfer market.