"Dejan, after three weeks he trained yesterday, a complete session with the team," Klopp told a news conference.
"It was good, but after three weeks we have to see."
Clyne was injured in Liverpool's 5-4 Premier League win against Norwich City on Saturday, meaning that Jon Flanagan could make his first start since the end of the 2013-14 season when he underwent two knee operations.
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"Clyney got a knock on the knee. He is a really tough boy, he is always available, but I think today it will not work for training," Klopp said.
"We have to see what will happen overnight and make a decision but it's not too easy because we have only Flanno.
"He is ready but of course it would be better if Clyney got fit."
Liverpool served up a thriller against Norwich and while their manager was pleased with his side's goalscoring efforts, he was less enamoured by their inability to defend set-pieces.
"It's not a problem we can ignore. It's obvious. We are always working on our weaknesses," he said.
"In Norwich, we defended the first ball well but struggled then with the second or third. It's not too late to learn. But now it's time to," he added.
Adam Lallana's last-gasp winner sparked wild celebrations on the sidelines at Carrow Road, and Klopp, who broke his spectacles in the melee, confirmed that he was wearing his second pair.
"It was my fault. No-one has to pay for them," the German said.
"Now I have to be careful. They are black and I look a little bit of a serial killer."
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
