Brendan Rodgers' team lost out in the reverse fixture late last year in a result that typified their inconsistent first half of the season.
However, last year's runners-up have embarked on a superb run since then, going 13 top-flight matches without defeat to put themselves firmly in the running for UEFA Champions League qualification.
Liverpool now sit just two points behind fourth-placed United, meaning this weekend's meeting could prove key in the race for the top four - and Rodgers is upbeat about his team's chances of avenging their defeat at Old Trafford.
"We've found solutions to issues we had at the beginning of the season but there is still a lot of work to do," Rodgers said.
"[The players are] very comfortable in the way of working. We showed a different side [in a 1-0 win] against Swansea on Monday and came through.
"[United have] got a lot of talent and had a big investment in the summer in world-class players.
"They've been up there all season, and they will want to stay up there. I don't worry about them clicking.
"They had a good result against Spurs [United won 3-0 last Sunday], but Anfield is a different game."
United, meanwhile, have lost just twice in the league since their derby defeat to Manchester City in November.
An impressive 3-0 win over Tottenham sets them up well for Sunday's clash, while Louis van Gaal has also been buoyed by the agreement of a new contract for Michael Carrick on Friday.
"I think every player knows the importance of this game. We are in a very crucial stage and cannot lose," said the Dutchman.
"We played very well in the first half [against Spurs] but it says nothing when you lose the next match.
"I want to win against them again. It's very important."
While Luke Shaw and Marcos Rojo are not fit enough to start for United, Rodgers can welcome back Lucas Leiva [groin] and Mario Balotelli [illness].
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