Drinkwater joined the Premier League champions from Leicester last summer for a fee of £35million, but has struggled to force his way into Antonio Conte's first-choice XI.
At this moment in time, Drinkwater has not featured in over a month, with his hopes of going to the World Cup this summer in ruins.
Drinkwater infamously turned down a call-up in November to focus on getting back fit but that decision has backfired, with a lack of game time loking set to put paid to his hopes of going to Russia.
Fellow midfielder Tiemoue Bakayoko has failed to shine since his own summer move from Monaco, but despite his struggles Drinkwater ahas still not been afforded any real chances.
The news that Jean-Michel Seri is also a target for the 'Blues' is thought to have further frustrated the former Manchester United trainee, who, according to English publication 'The Daily Mail', is now seriously considering his future.