According to reports from the Express, the 28-year-old could make his exit as soon as the January transfer window comes around, with Southampton and Drinkwater's old club Leicester keen to make a deal happen.
Leicester reportedly enquired with Chelsea in the summer about a possible transfer for Drinkwater but were unable to agree a deal before the transfer window closed.
Drinkwater partnered with N'Golo Kante in midfield of the Leicester side that won the Premier League title in 2016, and since then both midfielders have made the move to Stamford Bridge. Whereas Kante has established himself as one of the first names on Chelsea's team sheet, Drinkwater has spent most of his time at Chelsea on the fringe.
Drinkwater's last start for Chelsea came in the Community Shield in a 2-0 loss to Manchester City. With the signing of Jorginho, a player Maurizio Sarri was desperate to bring with him to Chelsea from Napoli, it is unlikely Drinkwater will soon break into the first team.
Leicester and Southampton are reportedly set to offer a loan deal for Drinkwater in January, and West Ham are also said to have been interested in snapping up the midfielder during the club's summer spending spree.
A move away from Stamford Bridge would surely be in the best interest of Drinkwater, who must be chomping at the bit for a first team opportunity.