The young Reds qualified for the knockout stages by topping Group E with five wins from their six fixtures against Maribor, Sevilla and Spartak Moscow.
Friday’s draw set up a home meeting with United for Steven Gerrard’s team, to be played as a one-off tie on either Tuesday February 20 or Wednesday February 21.
The winners will progress to a quarter-final clash away from home against either Manchester City or Inter Milan in mid-March.