White and Havertz scored braces to batter their London rivals 5-0
Jota was injured close to the end of Liverpool's 1-1 draw in the Champions League.
"Yeah, it's worse than we first thought and better than we then thought," Klopp said before kickoff in their Premier League clash at Fulham on Sunday. "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. It's pretty similar with Kostas Tsimikas, by the way. Unbelievable."