And it is reported that Leicester are becoming resigned to losing the homegrown talent.
Leicester have told Chelsea that they want a fee of around £75m, similar to what Manchester United paid for Harry Maguire a year ago.
Chilwell is under contract with the Foxes until 2024 and earns £65,000-a-week, a salary Chelsea would improve.
Chelsea will look to fund the deal by selling either Marcos Alonso or Emerson Palmieri.
Brendan Rodgers is looking at Southampton’s Ryan Bertrand as a possible replacement for Chilwell.
The Leicester boss coached Bertrand, 30, during his time at Chelsea’s academy and on loan while in charge of Reading.
However, Southampton are likely to resist any bids for Bertrand, a player they value highly.