Mahrez was given extra time off by the Foxes after playing in Algeria's worldwide games in June and had been set to return to pre-season training before confirmation of his move to City.
According to Sky Sports News, Leicester will receive around £60m for Mahrez, some way short of the East Midlanders' £80m asking price at the start of the year.
Mahrez helped Leicester to a shock Premier League title triumph in 2016, scoring 17 times, and then played a major role in the club reaching the Champions League quarter-finals during the following campaign.
According to the Daily Mail, the Algerian worldwide is set for a medical at Manchester City between Sunday and Tuesday.
Initially it looked as though the failed deal would wreak havoc when Mahrez went AWOL and failed to turn up for Leicester training for 10 days, but he soon returned and pledged his commitment to the club.
Good signing for Leicester City? Leicester said in a statement the deal was a "club-record fee".
"Riyad is a hugely talented player".
Mahrez's experience of winning the Premier League will certainly have left him hungry for more success, and he now has the chance to achieve that once more under the stewardship of Pep Guardiola.
"Watching them from afar has been a pleasure".
"I think we can be successful over the coming years and I believe my own game can develop under Pep's management".
Interestingly, the Algerian was back in Leicester's good books as he netted four more goals for the Foxes, taking his total goals to 39 goals from 139 top flight games for the King Power dwellers.