The former Manchester United midfielder is competing against the likes of Jorginho, N’Golo Kante, Mateo Kovacic, Cesc Fabregas, Ross Barkley and Ruben Loftus-Cheek at Stamford Bridge.
The Daily Star says Chelsea boss Maurizio Sarri is happy for the England international to leave before the European transfer window closes at the end of the month.
Drinkwater was not part of the Chelsea squad for the game against Huddersfield on Saturday.
The 28-year-old joined the Blues from Leicester in a £35million deal last summer.
