According to Jack Gaughan of the Daily Mail, the Algeria international now "looks destined" to make the switch to the Etihad Stadium this summer, with City manager Pep Guardiola said to be keen to secure some early signings.
"Mahrez, not at the World Cup, should enjoy a full pre-season to acclimatise to Guardiola's methods, with City heading for Chicago, New York and Miami in July," Gaughan wrote. "Napoli midfielder Jorginho will also be in the United States should City secure his signature in the coming weeks."
It's noted Guardiola doesn't want to get involved in a "mad scramble" for players at the end of what is a shortened transfer window for Premier League clubs.
A payment structure for Mahrez has reportedly yet to be finalised, although it appears the amount will exceed the club-record fee of £57 million City paid to secure the signing of Aymeric Laporte from Athletic Bilbao in the January transfer window.
Mahrez was linked with a move to City in January after the Premier League champions opted against pursuing Alexis Sanchez.
James Robson of the Manchester Evening News outlined why City want to bring in a player of Mahrez's style:
The 27-year-old has become one of the most effective wide players in the top flight in recent seasons, shining on the right flank.
Mahrez can be devastating when drifting off the touchline into dangerous areas, as he possesses exceptional balance, a burst of speed and excellent technical ability.
Per Sky Sports Statto, alongside Jamie Vardy he's been effective for Leicester:
So much of the excellent attacking work done by City last season came through the penetration offered from Raheem Sterling and Leroy Sane in wide positions. But if either was rested, injured or suspended, City sometimes lacked that dynamism on both wings.
Mahrez would provide that extra competition, and given how he floats infield, he would give Guardiola a different attacking option to Sane and Sterling.
Grup14's Rafael Hernandez believes the acquisition fills one of the few holes in City's squad:
Despite the money to be paid, Mahrez may not be a guaranteed starter for City with Sane and Sterling also in the squad, not to mention Bernardo Silva. But he's someone who can make a massive impression for the champions as they go in search of four trophies in the 2018-19 campaign.