The Premier League winners have been chasing the Algerian for more than a year and were close to signing him in January.
Mahrez, 27, is desperate to leave the King Power Stadium and was excused from pre-season training earlier this week as he closes in on his move to the Etihad.
As SunSport revealed in May, Leicester were willing to accept £60m – still a club record buy for Man City – in this window with Mahrez making it clear he would not return for the Foxes.
Sky Sports are now reporting the 2016 Premier League Player of the Year will have a medical this week.
Mahrez had handed in a transfer request and agreed terms with Man City in January, but the deal collapsed when City refused to pay the £90million asking price.
After the move fell apart, Mahrez went on strike, missing training sessions and matches.
In January, a close friend said the star was "very depressed" over not being allowed to move.
An anonymous source said at the time: "This is the fourth transfer window in which Leicester have said they will not allow him to leave.
"He feels very strongly that he has done everything in his power to help the club.
"He played a huge part in his first season, he then helped to make history by winning the Premier League title and he has done what the chairman has asked of him, which was to secure the club’s Premier League safety.
"They let [N'Golo] Kante go, [Danny] Drinkwater go — he could have been the record sale in the history of the club.
"By my calculation, Leicester could have made £59.8m profit on him. He has been told by former team-mates to get out of Leicester.
"He has given his all this season so he could leave in this window.
"Joining Manchester City would be a dream for him — playing for Pep Guardiola is something he is still desperate to do.
"He is very down about the way he has been treated by a club he has served so well."
Mahrez eventually returned to action for Claude Puel, after missing two matches after the row, finishing the season in good form.
Mahrez was the star man for Leicester City when they shocked the world to win the Premier League in 2015-16.
He was named Player of the Season after scoring 17 goals and adding 11 assists.
Last season he scored 12 goals and added 10 assists as the Foxes came ninth.
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