Blues boss Antonio Conte has held talks with the Algeria international, according to Tribal Football.
And the Premier League champions are prepared to bid £46.5m for his services.
Mahrez is the third Leicester star to pop up on Chelsea’s radar this summer.
Stamford Bridge chiefs are in negotiations to sign midfielder Danny Drinkwater.
Striker Jamie Vardy has also been linked, with Conte wanting another striker.
Mahrez fancies a move away from the King Power Stadium in search of Champions League football.
But Chelsea face a race against time to land Mahrez before Thursday’s transfer deadline.
According to Tribal Football, they are prepared to offer him a bumper pay-packet to make the move.
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Serie A giants Roma are also interested but are yet to agree a deal with Leicester.
Earlier this month, Foxes boss Craig Shakespeare admitted that Mahrez wanted out.
“He wants to play for a top-six club," Shakespeare said. “If we don’t get an offer from a top-six club, he stays. If that offer comes in and it’s not enough, he stays. It is quite clear for me at the moment, he has made that statement but he is our player.”
Mahrez, 26, has provided two assists in three appearances for Leicester this term.
He has three years left on his current deal.