The Giallorossi were paired with the English side, in what will be a repeat of the 1984 European Cup final, during Friday's draw in Nyon.
The first leg will take place at Anfield on Tuesday 24 April, with the second leg at the Stadio Olimpico coming on Wednesday 2 May.
The other semi-final sees Bayern Munich face holders Real Madrid.
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“It feels like a great opportunity to chase the joy that we were not able to experience so many years ago,” club sporting director Monchi said. “But of course it will be difficult, because Liverpool are an extremely strong side.
“We need to think about ourselves, and reproduce what we were able to show against Barcelona.”
Chief executive Umberto Gandini added: “We have the desire to play for our city and for Italian football.
"We will prepare for this as well as we can, with humility and focus. It’s important to play a good game at Anfield, after which we have the slight advantage of playing the second leg at home – where we will have the great passion of our fans to push us on.”
Liverpool beat Porto (5-0 on aggregate) and Manchester City (5-1 agg) to reach this stage.
“Who we got in the draw mattered little: all the sides at this point are great," club captain Daniele De Rossi said. "Liverpool have made a statement like we did, they beat the side that I thought were the favourites.
"They have a great coach. Like Barcelona and Shakhtar, we have huge respect for them – but we have a chance.”
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