The Sky Sports News reporter has claimed that the Blues are keen on bringing the England midfielder to Stamford Bridge this summer as Antonio Conte prepares for his second season in charge at the club.
Chelsea are believed to be keen on signing Drinkwater after the Blues let Nemanja Matic move to Manchester United on Monday.
However, although Drinkwater is believed to be one of Chelsea’s prime midfield targets this summer, Gilmour has also claimed that Leicester City are determined not to sell him.
Speaking on Sky Sports News on Tuesday morning, Gilmour said: “According to Sky Sources, Chelsea are interested in signing Danny Drinkwater as a replacement for Nemanja Matic.
“The England midfielder only signed a new four-year contract last summer.
“Leicester are under no pressure to sell Drinkwater and they say he’s not for sale, that’s their stance.”
Chelsea have made four signings so far this summer as Conte prepares his team for a return to the Champions League next season.
The west London side won the Premier League title in style last term as they claimed a record 30 victories on their way to lifting the trophy.
The Blues are now preparing to take on Arsenal in the Community Shield at Wembley on Sunday afternoon as they look to gain revenge over the Gunners for their FA Cup final defeat back in May.
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