The midfielder was forced off during the first half of Liverpool's 0-0 draw with City at Anfield on Sunday.
Speaking post-match, Klopp confirmed Milner has a hamstring issue, but the No.7 needs to be assessed before its seriousness is known.
"How much [serious]? It's too early, I don't know," said the manager.
"I asked him 'big one?' and he said 'I don't think so, but big enough that I go off.'"