Sane is expected to be out for up to seven weeks after damaging his ankle ligaments in the FA Cup win over Cardiff at the weekend, leaving City short out wide.
With the minutes until the closing of the transfer window ticking away, Pep Guardiola has moved to reinforce his side, reportedly bidding £50m for Algerian Mahrez.
'The Foxes' are understandably keen to keep hold of their star man, but the player is thought to have his heart set on the move, with the chance to work under Pep Guardiola too good to turn down.
With that in mind 'The Daily Mail' reports that Mahrez will slap in a transfer request in a bid to push through a switch to the Etihad.
The same souce claims that the 26-year-old did not report for training on Tuesday morning.
Losing Mahrez would be a bitter blow for Leicester, with the player having scored nine goals and laid on nine assists so far this season.
Leicester boss Claude Puel was recently quoted saying that he is confident Mahrez will remain a Leicester player, but with his head turned, it could prove increasing difficult to keep him happy.
Mahrez was named PFA Player of the Year during the 2015/16 season after joining the club for a bargain £450,000 in 2014.