The Brazil international had a scan on his right ankle on Monday after being carried off on a stretcher in Saturday's win over Sunderland.
Klopp has now confirmed the predicted diagnosis that the 24-year-old will probably be out until the new year.
The Reds boss: "We will see. He is out for the next few games."
Coutinho has been Liverpool's most influential player this season but Klopp said on Monday they could cope without him.
"It is no excuse for anything. As good as he is he does not decide games by himself, although it sometimes looks like this," the German said.
"It is a team performance we create and he is a very important part of this team, absolutely.
"Of course we can handle it. If he is not in you have to show - and we will show."