Sky Sports is reporting that the Premier League champions are interested in the England international as Antonio Conte looks to reinforce his midfield options.
The same article states that the Chelsea boss wants to add further depth following the sale of Serbia international Nemanja Matic to Manchester United in a £40m deal.
However, according the British media outlet, Leicester would be unwilling to allow the 27-year-old Premier League winner to leave the King Power Stadium this summer.
Drinkwater signed a four-year contract last summer after the midfielder helped the Foxes win the top-flight crown against the odds under ex-manager Claudio Ranieri.
The English star scored one goal and made one assist in 28 appearances in the Premier League last season as Drinkwater endured an alarming drop in form.
Conte has already signed France midfielder Tiemoue Bakayoko in a £40m deal from Ligue 1 champions AS Monaco this summer.
The Chelsea manager’s current midfield options include Bakayoko, Cesc Fabregas and N’Golo Kante with the Premier League set to start in less than a fortnight.
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