Leicester have granted Mahrez a week off after a friendly global with Algeria, but it is believed that the Foxes granted the extra rest for Mahrez to finalise his deal with City.
Leicester will receive around £60m for the Algeria worldwide - some way short of their £80m asking price in January.
The Citizens are thought to be paying £60 m for the 27-year-old.
The 2015-16 PFA Players' Player of the Year was not due to return to pre-season training with Leicester for another fortnight. City made a number of bids for Mahrez in the last transfer window as well.
Wales appoint Pivac as coach to succeed Gatland
If he is appointed, it will be a return to worldwide coaching for Pivac, who was Fiji boss for three years from 2004-2007. The New Zealander has won three Six Nations championships, including two Grand Slams since taking over in late 2007.
Mahrez scored 17 goals in that campaign, and then having signed a four-year contract, played a major role in the club reaching the Champions League quarter- finals in 2016/17 as he contributed four goals.
Mahrez joined Leicester City in 2014 from French side Le Havre for a fee believed to be in the region of £400,000.
Manchester City have also been linked with Napoli midfielder Jorginho with the Italy worldwide reportedly left out of their pre-season training camp squad.
Regardless of being at odds with the Foxes, Mahrez managed to score 13 goals in 41 appearances last season and Manchester City boss Pep Guardiola feels that he is the missing cog in his team.