While the Citizens are not willing to go that high, they seem to hope that the addition of a player in the other direction will persuade Leicester to finally part with the 26-year-old.
That will surely depend on the player, with Sky Sports unaware of his identity.
The most likely candidate appears to be defender Eliaquim Mangala, who is available after City’s capture of Aymeric Laporte and had been expected by Sky Sports to join Everton.
The Foxes do not have great depth at centre-back, with title-winning pair Wes Morgan and Robert Huth both nearing the end of their careers, and Mangala would arguably be an improvement on loanee Aleksandar Dragovic.
As BBC Sport reports, Mahrez has handed in an official transfer request at the King Power Stadium - the second time he has done so in six months - to try to force through a move.