Sky Sports News understands City have offered Leicester in excess of £50m for Mahrez and it is believed this is their second bid for the Algerian winger during this window.
Speaking earlier this month, Foxes boss Claude Puel insisted Mahrez would not be allowed to leave the club in January. However, Leicester denied both before Mahrez handed in his transfer request.
With Sane injured for at least six weeks, Guardiola will want to add more depth to his attack at Manchester, after missing out on buying Alexis Sanchez who went to rivals Manchester United this transfer window.
However, according to talkSPORT sources, Mahrez has submitted a formal transfer request in a bid to force through a late move to the Etihad Stadium.
Shall Guardiola somehow pull this deal off, it would quite possibly be the most astonishing transfer of the winter, simply because the league leaders have not once been linked to Riyad Mahrez, with Liverpool and Arsenal in particular being the favourites for the 26-year old.