Solskjaer is winless in five league games against Klopp's LiverpoolManchester United boss Ole Gunnar Solskjaer says his side are "striving" to emulate Liverpool's success over the past four years as the rivals prepare to meet at Old Trafford on Sunday.
Liverpool have won the Champions League and Premier League since United's last trophy, the Europa League in 2017.
Solskjaer is yet to beat the Reds in the league as United boss.
"It's going to take everything to get a result against one of the best teams in Europe and the world," he said.
"And Liverpool are one of those. They are one of the teams we are trying to chase because what they have done in the last four years is something we are striving towards and go past them.
"We did end up above them last season, but they had a very bad spell of injuries and now they are back to their best."
Liverpool go into Sunday's encounter at Old Trafford as the only unbeaten team in the Premier League after five wins and three draws from their opening eight games.
United are four points adrift of Jurgen Klopp's side having taken just one point from their last three league outings.
"A performance needs to consist of 90-plus minutes of attacking and defending against a team the level of Liverpool," added Solskjaer, who revealed that Bruno Fernandes is among his injury concerns for Sunday.
"At the moment they are on a great run of form with some individual skills that you cannot almost defend against, but as a team we have to be compact and aggressive."
Atalanta comeback can spark 'something big'
Ronaldo's late header completed United's stirring fightback in the 3-2 win over AtalantaSolskjaer's position has come under renewed scrutiny in recent weeks after United followed their Carabao Cup exit at the hands of West Ham by taking one point from league games with Aston Villa, Everton and Leicester.
The Norwegian's position was in danger of being further weakened on Wednesday when United fell 2-0 behind in their Champions League Group F meeting with Atalanta, only to secure a dramatic 3-2 win following a superb second-half comeback.
And Solskjaer says he hopes that result will be the start of "something big" before a daunting period that will see United face Liverpool, Tottenham, Atalanta and Manchester City in their next four games.
"It's something we have done plenty of times at the club," the 50-year-old said when asked about Wednesday's comeback.
"It's in our DNA, it's never give in, Sir Alex's documentary - that's what our fans expect from us, to give everything you have, give your best all of the time and when you do that with the quality of the players you have here you can win and lose games, but come out of it having given everything and know that's a team out there.
"I saw a team in the first half as well [against Atalanta] that gave everything for each other, but we needed half-time to maybe push that belief a little bit more.
"We kept on believing in what we're doing. Hopefully, it's the end of a bad period for us, a bad spell.
"Teams always go through bad spells and good teams come together and hopefully this can be a start of something big."
Solskjaer 'will always back Ronaldo'
Salah has scored 12 goals already this season, including two against Atletico Madrid on TuesdayUnited have kept just one clean sheet in all competitions this season and their defence is likely to be given a stern examination by in-form Liverpool forward Mohamed Salah on Sunday.
When asked about comparisons between the Egyptian and United forward Cristiano Ronaldo, Reds boss Klopp said they are "both world-class players".
Salah has scored 12 goals in 11 games this season with Ronaldo netting six times in eight, but Solskjaer said he would back the Portugal forward "in any competition".
"His [Ronaldo's] goalscoring record is incredible and he just keeps on scoring. That being said, Salah, at the moment, he's on fire.
"You see some of the goals he's scored lately. We know we have to be at our best to defend against him.
"You know, players like this don't come around very often and we have to enjoy them from afar, not on Sunday, that's too close for me."
