The Brazil international was caught by Didier Ndong's follow-through half an hour into the game and later left Anfield on crutches with his right foot in a protective boot, but he will not be able to be scanned until Sunday at the earliest.
Coutinho has played a major part in Liverpool's emergence as title challengers this season and is their leading scorer with six goals, having created countless other chances.
With another creative player in Adam Lallana still sidelined with a groin problem they can ill-afford another absence, especially after Roberto Firmino was forced off late on with a calf problem with striker Daniel Sturridge missing the game with a similar injury.
"We have to wait for the scan. What we know it is something with the ankle," said Klopp. "He had pain. Pain gets better. In the first moment it was very painful but at half-time he said it was better.
"I am quite an optimistic guy so I hope he can train tomorrow."