The former Southampton midfielder been one of the most reliable performers for Klopp's side this season.
Lallana is expected to be out for a month, having suffered the injury during the closing stages of England's 2-0 victory over Lithuania at Wembley last Sunday.
The former Southampton midfielder been one of the most reliable performers this season in a Liverpool side who have lacked consistency, and his absence will be felt keenly as Reds boss Klopp attempts to secure a top-four Premier League finish.
They sit fourth going into the weekend's fixtures, with a four-point advantage over Manchester United in fifth.
United do have two games in hand, but that is no guarantee that they will make up the gap, as they have matches at Manchester City, Arsenal and Tottenham before the end of the season.
Liverpool's form going into the international break was encouraging; home wins over Arsenal and Burnley were followed by a draw at Manchester City, and they will start favourites against Everton, who have not won at Anfield since September 1999.
Sadio Mane's goal in the seventh minute of stoppage time gave Klopp's team a 1-0 victory in the reverse fixture at Goodison Park in December, and a win on Saturday would secure a first league double over their local rivals since 2011-12.
Liverpool will be helped by the likely return of Jordan Henderson after more than a month out with a foot injury, with the England midfielder having resumed full training during the international break.
Klopp is in no doubt that Champions League qualification is in Liverpool's hands.
"In this moment, we should only think about how we can do it," he said.
"Would it be a disappointment if we don't reach it? Yes because we think we should qualify for it.
"Is it possible that we don't qualify? Yes because of the league, because of the opponents and all that stuff.
"But it is our big target, of course. We want to do everything to get it."
Everton have injury problems of their own as they make the short trip to Anfield without defender Seamus Coleman, who broke his leg in horrific circumstances while playing for the Republic of Ireland last week.
Coleman is likely to be out for between nine and 12 months after his tibia and fibula bones were broken in an awful challenge by Wales defender Neil Taylor during the 0-0 draw in Dublin.
Images of the challenge showed just how bad the injury was, although the Everton right-back had successful surgery last Saturday, and the club are confident that he will make a full recovery.
That was not the only injury setback for Everton during the international break, with midfielder James McCarthy suffering a recurrence of his persistent hamstring problems while with the Republic of Ireland, and having to be withdrawn from the side to face Wales shortly before kick-off.
Despite those problems, Ronald Koeman's side are in good spirits, lying seventh, just six points behind Liverpool, having lost only once in 12 league matches since the two sides last met.
Everton have not beaten Liverpool home or away since October 2010, enduring a run of 13 derbies in all competitions without victory.
However, Koeman is optimistic, saying: "There has been a big difference in many years in derby results, but I think we are now more close to Everton beating Liverpool.
"We had a good game at home and were only defeated by a goal in the 97th minute.
"The team will be ready on Saturday to give Liverpool a big challenge."