The Reds were pitted against their bitter Premier League rivals for the first time in Europe in Friday’s last-16 draw.
Jurgen Klopp’s side secured their place in the next round thanks to a 1-0 win against Augsburg on Thursday night thanks to James Milner’s fifth-minute penalty.
Louis van Gaal’s side, meanwhile, were 5-1 winners against FC Midtjylland after a 2-1 loss in Denmark.
Former Liverpool striker Aldridge is feeling optimistic about the 18-time English champions’s chances of securing victory over two legs which will be played on 10 and 17 March.
“While it will be a couple of nervy games for certain, for me it’s a great draw. I’m delighted,” Aldridge told Liverpool Echo.
“Why? Because I think we can beat them over two legs.
“I’m glad the first game is at home. If we can keep a clean sheet at Anfield, then I fancy us to go there and get the job done to be honest.
“It’s massive for both clubs, the first European meeting. They’ve done us over twice this season; let’s hope it’s our turn now!”
Liverpool lost 3-1 to the Red Devils at Old Trafford in September as Anthony Martial scored his first goal for the 20-time English champions.
The Reds lost 1-0 against Van Gaal’s side at Anfield in January after Wayne Rooney’s late winner.
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