The 30-year-old has not played for Chelsea’s first team in almost two and a half years, having last appeared in August 2018.
Drinkwater had loan spells at Burnley and Aston Villa last term, only appearing this season with Chelsea’s under-21 and under-23 sides.
He still has 18 months of his five-year contract with Chelsea remaining.
Drinkwater, capped three times for England, helped Leicester City win the Premier League title in 2015-16, but has failed to make a significant impression at Stamford Bridge since making his £35m move in 2017.
He has made 23 appearances for the west London club, but not since their Community Shield defeat by Manchester City in 2018 when he came off the bench.
Two loan stints with Premier League rivals Burnley and Aston Villa last term were short lived, with him featuring just twice for the Clarets and four times for Villa.
His spell at Villa was controversial and he did not play for the club again after clashing with team-mate Jota at the club’s training ground in March.
Drinkwater this season featured for Chelsea’s under-21 side in the Papa John’s Trophy and was sent off when playing for their under-23s in a Premier League 2 match against Tottenham in December.
