Klopp not wishing Salah too much luck at Africa Cup of Nations
Salah is away with Egypt for the tournament in Ivory Coast while Japan captain Wataru Endo will be involved at the Asian Cup in Qatar, with both players expected to go deep in the respective competitions.
That could mean they will not be back until the second week in February but Klopp said he sent them on their way this week without wishing them too much success.
"I said if I wish you good luck it would be a lie," Klopp said ahead of Liverpool's FA Cup third-round tie at Arsenal on Sunday.
"From a personal point of view, I would be happy if they go out in the group stage but that's probably not possible. They can go on and win it.
"So it was 'Good luck and come back healthy'. We have to deal with it and we will deal with it. I am pretty positive that we will find a way."
Klopp does not really have a suitable replacement for Salah, who plays on the right side of his attack and has scored 18 goals in all competitions this season.
Midfielder Dominik Szoboszlai was touted as a potential option but he has been ruled out for at least two matches with a hamstring injury sustained in the New Year's Day win over Newcastle.
But Klopp, whose side are top of the Premier League, is confident Liverpool can fill the hole left by Salah.
"I think we played against West Ham (in last month's League Cup quarter-final) without Mo on that side and Harvey Elliott played there," he said.
"We have different offensive options who can all play that wing in a different way. Nobody else can play like Mo, it is not possible -- we just have to use the boys with their skills.
"Do we want to play without Mo? No. In the past we didn't have to do it often but we always found a way.
"But we play Arsenal and you can lose to Arsenal with Mo Salah so it's possible to lose to them without him."
Klopp said he was braced for a challenging January, even though there are fewer Premier League games due to a mid-season player break.
Liverpool's game at the Emirates comes just two weeks after the title-chasing sides drew 1-1 at Anfield in the Premier League and will be followed by the first leg of their League Cup semi-final against Fulham on Wednesday.
"Some teams obviously don't play that often in January," he said. "We don't have that, we have now with the semi-final, we have a proper rhythm.
"I think a re-match against Arsenal would really not be helpful, that's how it is, because it just doesn't fit in, would kill the winter break, stuff like this."