Pep Guardiola's side came close to signing the Algerian in January, only to see a perspective move collapse at the 11th hour.
In the end, there proved to be an unbridgeable gap in the valuations of the two players, with Leicester holding out for a package worth £95m and City valuing the player at closer to £60m.
The collapse of the seal led to Mahrez going on a self-imposed strike, whilst he also slapped in a transfer request.
Despite subsequently apologising for his actions, it is understood that Mahrez would still be keen on the switch if City were to revisit a deal this summer.
Guardiola has made it clear he will only be performing minor surgery on his squad, with one or two world-class additions the order of the day at the Etihad.
Napoli midfielder Jorginho is another player to have been linked with the champions, who are in the market for a replacement for the outgoing Yaya Toure.