The Portuguese forward was not involved in the club's Premier League draw with Fulham on Sunday, due to an injury he suffered in midweek.
The attacker has a knee injury that he sustained in the team's 1-1 draw with Midtjylland on Wednesday.
"It's worse than we first thought but better than what we (later) thought. The potential surgeons had a look at it and no surgery is needed, but he will be out for a while," Klopp told Sky Sports.
"We don't know exactly, but we think one and a half, two months.
"In the end it was strange, but we were happy when we heard the final diagnosis."