Drinkwater joined the Blues for £35m last summer but struggled with injuries and made only five starts in the Premier League, failing to break into the team ahead of the likes of Cesc Fabregas, Tiemoue Bakayoko and former Leicester teammate N'Golo Kante.
Chelsea have now added to their ranks in midfield even further with the capture of Italian Jorginho from Napoli - and have been linked to Arsenal's Aaron Ramsey - weakening Drinkwater's chances of playing next season even further.
England international Ruben Loftus-Cheek has also returned to Stamford Bridge after spending last season on loan at Crystal Palace and will almost certainly move ahead of Drinkwater in the pecking order too.
Drinkwater has suffered a spectacular fall from grace in his year at Chelsea, having made a name for himself as a key part of Leicester's 2015/16 Premier League title-winning side next to Kante in midfield.
Having worked his way into the England setup under Roy Hodgson, the 28-year-old was nowhere near current Three Lions boss Gareth Southgte's plans for the World Cup this summer after scarcely featuring for Chelsea all season.
Southampton and Crystal Palace are rumoured to be interested in Drinkwater, potentially on loan.
However, it remains possible that Drinkwater could stay at Stamford Bridge due to his ability to help fill the club's home-grown quota for the season, though the chances of this are slim after the club signed veteran goalkeeper Robert Green from Huddersfield.