The pair will face each other in the last 16 in what will be the clubs’ first tussle in Europe.
The first leg is at Anfield on Thursday March 10 at 8.05pm, with the return at Old Trafford the following week in a 6pm kick-off.
The powder-keg ties will present a huge security headache for police in both cities.
Extra officers will be drafted in to combat the threat of violence between rival fans.
Starsport understands officials from both clubs will meet next week to discuss security arrangements for the respective games.
But Reds boss Jurgen Klopp has fanned the flames ahead of the showdown by insisting his side is out for revenge.