Drinkwater is currently on his third loan spell away from Stamford Bridge since joining Chelsea from Leicester City in the summer of 2017 for £35m.
The 31-year-old former England international joined Turkish Super Lig side Kasimpasa on a loan deal until the end of the 2020/2021 season after similar unsuccessful temporary spells at Aston Villa and Burnley.
Drinkwater has made just 23 appearances for Chelsea since his big-money move from the King Power Stadium, where he won the Premier League in the 2015/2016 season.
After failing to make the grade under Maurizio Sarri and Frank Lampard, Drinkwater is hopeful he will be given a second chance under Thomas Tuchel when his loan spell in Turkey comes to an end.
"I want to continue with Chelsea. I feel like I have unfinished business with this club," Drinkwater said during an interview with Hany Hathout on the Elmatch Program.
Asked if he believes he can rediscover his best form and force his way into Thomas Tuchel's current Chelsea squad, the midfielder added: "I would like to think so. I don’t know if it is a good idea to go back to Chelsea and start declaring these things. I have got a long way to go.
"I have to try and start enjoying my football again because in this moment it has disappeared. I keep working hard, I keep grafting and I am doing the right things at the right times and I need to stay injury free and see where it takes me.
"It is a short career so I need to keep doing the right things and hope things turn around."
Drinkwater has made seven appearances for Kasimpasa since joining them on loan.
