"All the potential surgeons had a look on it, no surgery needed. But he will be out for a while. We don't know exactly but one-and-a-half, two months. We don't know exactly."
Klopp had also said that reserve defender Kostas Tsimikas had suffered a knee injury similar to Jota.
Klopp was dealt a further injury blow during the Fulham match with central defender Joel Matip withdrawn at halftime after suffering a back problem.
"Joel has a spasm in his back," Klopp said. "We will see. He will get treatment and we will see. I think there will be a chance for Wednesday [against Tottenham Hotspur]."
Jordan Henderson dropped into central defence against Fulham and Liverpool are light in the central defensive area.
"I hope Joel will be fine, but I don't know. We will have to find a solution. That's how the football season is," said Klopp.