The Algerian winger reportedly did not turn up for training on Tuesday and chose not to inform anyone at the club of his absence.
It left manager Claude Puel unsure of what was happening, and could disrupt the Foxes' plans for Wednesday evening's game at Goodison Park.
This comes after Sky Sports reported that City have made a fourth and final offer for Mahrez, believed to be worth £65m including - or plus, depending on who you listen to - an unnamed player.
The Algerian's rebelliousness has reportedly left Leicester now seriously considering selling him before the close of the transfer window.
Puel had expected the in-form attacker to start and had prepared his tactics with that in mind. But he has been forced into a late change, with another player promoted to the first-team having been under the impression they were going to be rested.
MAHREZ LATEST— Sky Sports PL (@SkySportsPL) January 31, 2018
Man City have made a final cash plus player offer to Leicester for Riyad Mahrez worth up to £65million, Sky sources understand
Deadline Day LIVE https://t.co/5BtXs9SvNp pic.twitter.com/1W32fcMbEM
(You may also be interested in
It was thought that the Foxes would demand in excess of £70m for Mahrez, but City's last offer may yet be deemed acceptable.
The 27-year-old has over two years remaining on his current contract at the King Power, having signed a new deal after the title-winning campaign of 2015-16.
Mahrez has scored eight goals and provided seven assists in 24 Premier League appearances so far this season.