The winger looks set to become the latest big-name export to the Saudi Pro League.
Al Ahli have agreed a £30million fee with City for the 32-year-old's services, who has already agreed personal terms with the club.
Mahrez has been given permission to not travel with the squad as they make their way to Japan and South Korea on a pre-season trip.
talkSPORT also understands the Algeria international informed Pep Guardiola that he wanted to leave City this summer.
It comes after the player was left out of both Champions League and FA Cup final starting line-ups.
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That left the former Leicester star, who made 47 appearances in all competitions last season, fuming.
In total, he scored 15 and assisted 13 times but Bernardo Silva started over him in both finals, which City going on to win against Inter Milan and Manchester United respectively. Mahrez didn't even manage an appearance off the bench in either match.
Guardiola is happy to see the forward leave this summer after Al Ahli matched City's asking price of £30m.
It will see Mahrez become the latest high-profile transfer in the Gulf State with Karim Benzema, N'Golo Kante and Ruben Neves just a few of the big-name players to make the move to Saudi Arabia.
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Steven Gerrard has also joined Al Ettifaq as manager, who himself is closing in on the signing of Jordan Henderson of Liverpool.
But Mahrez's impending departure comes amid a small exodus at the Etihad Stadium and City are considering venturing in the transfer window to find a replacement.
While the wing wizard is the only senior player not making the trip to Asia, several players have been linked with transfers away.
Kyle Walker is closing in on a move to Bayern Munich while Joao Cancelo could also depart after spending the latter half of last season on loan at the Bundesliga club.
Aymeric Laporte and Silva could also leave, as well as back-up goalkeeper Zach Steffen.
Mahrez has won four Premier League titles with City, as well as the Champions League and FA Cup last season.