The England midfielder is understood to want to move to Stamford Bridge but the West London club have failed to meet Leicester’s valuation so far, with a fee of £25m having been discussed.
The Foxes do not want to sell their prize playmaker and Sky Sports News understands it will take an exceptional offer in excess of £30m to prise him away from the King Power Stadium before the deadline.
Sky sources understand the later a new offer is made for Drinkwater, the more reluctant Leicester will be to sell, because of the difficulty they would have in finding a suitable replacement at short notice.
Chelsea have already signed combative midfielder Tiemoue Bakayoko from Monaco this summer but Blues manager Antonio Conte wants Drinkwater to bring something different to the team.
The champions also sold Nemanja Matic to Manchester United – something Conte was reportedly not on board with – and Drinkwater has been highlighted as a possible replacement for the Serb.
Drinkwater only recently signed a new four-year contract but he would also be reunited with former Leicester team-mate N’Golo Kante should he move to Stamford Bridge.
The pair starred alongside each other as Leicester clinched the Premier League title in 2015-16.
New signing Bakayoko insists he is not threatened by the possibility of Drinkwater joining Chelsea.
“Competition only makes you better. I am not scared of anyone,” Bakayoko told French media SFR Sport. “I think that there are not enough of us in midfield, especially with all the competitions we will be playing in.
“We need another midfielder to reinforce the team, so it is a very good thing that he could be coming.”
