Roma, Arsenal and Barcelona have been linked with the Algerian international over the past few months.
The 2016 PFA Player of the Year released a statement at the end of last season confirming that he wants to leave the King Power Stadium.
Roma reportedly withdrew their interest in the 26-year-old earlier this month after having a handful of bids rejected, but it is believed that Chelsea are keen to get a deal over the line before tonight's 11pm cutoff.
According to beIN Sports, the Premier League champions and Leicester have agreed a £45m fee, which would allow the Blues to discuss personal terms with Mahrez.
The winger has started all three of the Foxes' league matches this season, and has provided two assists.