The England international who plays as a midfielder for premier league club Leicester City and England international team is viewed as a perfect replacement for Nemanja Matic who has sealed his transfer to Manchester United.
The 27-year old Drinkwater, who would also boost Chelsea's homegrown contingent, signed a four year contract at Leicester and is key to Craig Shakespeare's plans.
The England international was a key figure in the Leicester City's title winning season 2015-2016 under former Leicester's coach Claudio Ranieri.
Though he would be interested in a move to Chelsea he is conscious he could end up with a peripheral role as Conte aims to pair Tiemoue Bakayoko with N'Golo Kante as his midfield engine room of choice.
New recruit Bakayoko though is doubtful for the start of the season following minor knee surgery.
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