"It would be cool. He is improving a lot," Klopp told British media when asked if Coutinho could be back for the clash against Manchester City at Anfield on New Year's Eve.
"He is off his crutches since the West Ham United game (on Dec. 11), when we left the stadium he was walking in front without them."
Coutinho said he has set his sights on making his return against City.
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Klopp, however, insisted the midfielder will not be rushed back into action.
"We will have to see," the German manager added.
"No idea at the moment. I never rush a player back. I'm the most patient person in Liverpool. I always wait for someone. I can't rush it."
In Coutinho's absence, Liverpool have had mixed results, having lost at Bournemouth and being held to a home draw by West Ham United before getting back to winning ways at Middlesbrough on Wednesday.
Liverpool, who are second in the league, are nine points behind leaders Chelsea but have a game in hand and face Merseyside rivals Everton at Goodison Park on Monday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
