This morning, Klopp was asked about Van Dijk's recovery after news of his successful surgery was confirmed earlier today.
"The surgery was successful, which is really good, the best news we could get," said Klopp.
"This time [after a operation] is always unpleasant. He is good as good as can be."
Klopp has confirmed Fabinho is ruled out of this weekend's game with West Ham due to a hamstring injury suffered in midweek, though the Reds boss wouldn't be drawn on a timescale for his recovery.
"Fab is not in, he has a little injury," said Klopp. "He's out for the weekend and slightly longer but all the others are in contention."
Liverpool have spoken to referee's chief Mike Riley about application of VAR during the incident that resulted in Van Dijk's injury, but Klopp would not reveal what was said and is keen to move on.
"I don't want to talk about this anymore. I would immediately if it would change anything but it doesn't," he said.
"I'm not sure the world is in a place right now where we have to keep this story going.
"Yes we still feel something about it, but nothing that will happen will change that. So I've nothing else to say."