Drinkwater has made little impact since joining from Leicester for £30million, and a loan deal would also be considered for the player.
The England international made only five appearances in the league for Chelsea, and has not made England's squad for the World Cup, only two years after he won the league with Leicester.
In addition, Chelsea are themselves looking at other midfield options, including Nice's Jean Michael Serri, to go alongside Cesc Fabregas, N'Golo Kante and Tiemoue Bakayoko.
Persistent injuries hampered Drinkwater in his first season, but if he can remain fit then a loan deal would probably the perfect spark to rejuvinate his career.