The 24-year-old was withdrawn midway through the first half at Anfield, after a strong challenge from Black Cats midfielder Didier Ndong, and was replaced by Divock Origi.
Speaking after the game, Klopp confirmed Coutinho’s issue was with his ankle, but remained optimistic over the playmaker’s recovery.
“We have to wait for the scan, what we know in this moment is it’s something with the ankle. That’s it, so we all have to wait,” he said.
“Pain gets better, in the first moment it was very painful, but already when I saw him at half-time he said it was much better.
“As I said, we have to wait. I’m quite an optimistic guy, so I hope he can train tomorrow!”
Reportedly, though, Liverpool don’t think Coutinho has suffered a fracture – which may or may not be a good thing, as ligament damage would see him ruled out for longer than a broken foot, for instance.
When asked about potential injury Firmino, Klopp said his condition was “much better than Phil,” but revealed that he had “pain in the calf.”
With Adam Lallana already sidelined, losing both Brazilians would be a bitter blow for Klopp as the Reds head into a busy December schedule.
This was only magnified as he admitted he had “no idea” when Sturridge would return from his own calf injury.
Coutinho is likely to undergo a scan on Sunday, with further updates over his injury due in the coming days.