The Premier League champions are looking to sign the England international from the 2016 Premier League champions before the close of the summer transfer window.
Chelsea have been linked with a move to sign the 27-year-old midfielder since Nemanja Matic completed a £40m move to title rivals Manchester United earlier this month.
The west London side were forced to rush back summer signing Tiemoue Bakayoko from injury to give Antonio Conte more options in his depleted midfield.
Drinkwater hasn’t featured for Leicester in the 2017-18 season so far due to a thigh problem amid continued talk of Chelsea signing the England international.
Sky Sports News reporter Aidan Magee has revealed that negotiations are ongoing between Chelsea and Leicester but the two clubs are some way apart in their valuation of the midfielder.
“We understand that Danny Drinkwater handed in a transfer request on Monday morning at the Leicester City training ground,” Magee told Sky Sports News on Wednesday morning.
“We’re told Leicester and Chelsea, though, are still a long way apart in their valuation of the player. Sky sources say Chelsea’s biggest bid so far is worth £23m.
“Leicester don’t want to sell him and it would take an offer well in excess of £30m for them to be tempted. Leicester are reluctant to sell due to the difficulty they’d have in finding a replacement.
“He still has the rest of this season and three more seasons remaining on his Leicester contract.”
Chelsea have already signed Manchester City goalkeeper Willy Caballero, AS Roma defender Antonio Rudiger, Monaco midfielder Bakayoko and Real Madrid striker Alvaro Morata this summer.
The west London side were 2-0 winners against Everton at Stamford Bridge on Sunday afternoon to follow up their 2-1 victory over Tottenham Hotspur earlier this month.
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