The Reds legend says a first-leg win is a must.
Anfield plays host this evening as Jurgen Klopp's side clash with their bitter Premier League rivals on the European stage, with a spot in the quarter-finals ultimately being up for grabs.
They come up against a rather depleted Red Devils side as far as injuries go, and Aldridge believes that only a win will do ahead of next week's return leg at Old Trafford, insisting home goals are vital.
"Away goals are so vital in European matches and I look at the United side right now and they have injuries all over the place. That has to give Liverpool a chance to beat them this time," he told The Sunday World.
"You will merely get a quarter-final place in the Europa League for winning this tie, but the mood among Liverpool fans is that this is a tie that can give an ordinary season for the club a memorable moment to cherish.
"European football under the lights at Anfield is always special, so what will it be like when Man Utd show up for battle? The hairs on the back of my neck are already beginning to stand up."
The Reds have already lost twice to United this season, with Klopp being in charge of the Anfield defeat back in January when Wayne Rooney netted the only goal.
It was Brendan Rodgers-managed Liverpool who lost 3-1 at Old Trafford earlier in the season, though the Merseysiders look a stronger team under the German - especially in big matches.
Under Klopp, Liverpool have done the double over Manchester City, by an aggregate of 7-1, and they also beat Chelsea while Jose Mourinho was in charge.