Blues boss Frank Lampard had put Chilwell high on his wanted list ahead of the transfer window opening after failing to get a deal done for the left-back in January, but the transfer fee the Foxes are looking for appears to be an issue.
Leicester are said to want the same amount that Manchester United paid for Harry Maguire back in the summer, and Chelsea will not go that high.
United ended up paying around £80million to get Maguire on board, but Chelsea do not want to pay that much for Chilwell and will look elsewhere unless the price comes down.
The Foxes will not drop their valuation.
They have shown on more than one occasion that they are not willing to let players go unless the figure they have in mind for a player is met, and the same applies to Chilwell.
Leicester are in a strong position as Chilwell is under contract until 2024 so they are under no pressure to sell and will hold out for the fee they are looking for.
Chilwell himself is also happy at the King Power Stadium and will not kick up a fuss in an attempt to try and force through a move to Stamford Bridge.
Taking all that into consideration, Chelsea have realised they are fighting a losing battle with this one and will now look to other targets as Lampard seeks to bring in another left-back.
Among the players said to be on the wanted list are Getafe's in-demand left-back Marc Cucurella and Porto ace Alex Telles, both of who would cost substantially less.
Chelsea will face strong competition though, with Barcelona among the clubs said to be showing an interest in Cucurella.
Lampard wants a new left-back as there is a chance both Emerson Palmieri and Marcos Alonso will be on the move this summer.