Having topped Group H with 12 points, Sir Alex's men can face any of the sides who finished as runners-up in the other groups, although Arsenal will be removed from the pot as UEFA regulations forbid teams from the same association facing each other in the Round of 16.
That means United will be paired with one of the following sides: FC Porto, AC Milan, Real Madrid, Shakhtar Donetsk, Valencia and Celtic.
ManUtd.com will have live coverage of the draw on 20 December (10:30 GMT). The first leg of the Last 16 fixtures - United will play away from home first - will take place on either 12/13 February or 19/20 February.
Speaking after the Reds' 1-0 defeat at the hands of Cluj on Wednesday night, Sir Alex didn't reveal which team he would prefer to be paired with, but said there were a number of potentially "appetising" games.
Possible Last 16 opponents:
Draw: 20 December