Article updated 12:08 (confirmed dates)
The Greek champions finished as runners-up in Group C behind Paris Saint-Germain, after securing their place in the knock-out phase with a 3-1 win over Anderlecht last Tuesday.
As winners of Group A, the Reds will have home advantage in the second leg of the last-16 tie. The away match will be played on 25 February and the return meeting will be at Old Trafford on 19 March.
The two clubs faced each other four times during the group stages of the competition in 2001/02 and 2002/03, with United winning all four fixtures.
Manchester City v Barcelona
Olympiacos v Manchester United
AC Milan v Atletico Madrid
Bayer Leverkusen v Paris Saint-Germain
Galatasaray v Chelsea
Schalke 04 v Real Madrid
Zenit St Petersburg v Borussia Dortmund
Arsenal v Bayern Munich