The Rossoneri are set to travel to Old Trafford on March 11, with the second leg at the San Siro provisionally taking place seven days later – Covid-19 travel restrictions permitting.
Like United, Milan currently trail cross-city rivals in their domestic title race, with a four point-gap to leaders Inter in Serie A as things stand.
The two illustrious sides have previously met 10 times in competitive European action, including in 2010, when David Beckham returned to Old Trafford in a heavy 4-0 Champions League last-16 defeat for Milan, who had already lost the first leg 3-2 in Italy.
United ensured their place in Friday’s draw with a straightforward victory over Real Sociedad in the Europa League round of 32.
Ole Gunnar Solskjaer’s side were held to a goalless draw at Old Trafford on Thursday evening, with Mikel Oyarzabal badly missing a penalty for the LaLiga outfit and 17-year-old Shola Shoretire becoming the youngest player ever to feature for United in a European game after coming off the bench for the final 15 minutes.
However, the damage had already been done on neutral territory in Turin seven days before, with Bruno Fernandes netting twice and Marcus Rashford and Daniel James also getting on the scoresheet during a 4-0 rout at the home of Juventus that should have been even more comfortable.
United will be hoping to go one stage further than last term, when one of their three semi-final defeats came in the Europa League against eventual champions Sevilla after a profligate display in Germany.
Milan, meanwhile, reached the last-16 by seeing off Red Star Belgrade on away goals in the first knockout round.