Conte is desperate for reinforcements and sees the 27-year-old as providing excellent competition in midfield.
The Blues have been targeting the England global and want to bring him to Stamford Bridge before tomorrow's deadline.
Chelsea manager Antonio Conte has set his sights on the England worldwide, alongside Alex Oxlade-Chamberlain and Ross Barkley, as he bids to add the finishing touches to the club's summer transfer window.
And Leicester forward Mahrez has been given permission to leave the Algeria squad and return to Europe to "formalise his transfer to his new club", with Chelsea said to be in the running.
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So if the champions are determined to lure him to London it is going to cost them a hefty fee.
It could turn out to be a triple swoop on the Foxes as Danny Drinkwater and Jamie Vardy also continue to be linked.
However, the player turned down Chelsea and signed for Liverpool and it now appears they're about to be snubbed again.
Complicating the situation further, Barkley has a serious hamstring injury which could rule him out for three months.
And that means the Blues have £40m in funds to splash out on the Premier League victor.