The Greek champions finished second in Group C behind Paris Saint-Germain and will now face United for only the fifth time - and for the first time since 2002.
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"We are very pleased that we are in this draw, we could not ask for anything more," he told the club's official website.
"We know what is happening right now. It's a celebration of football for us, even more so to visit a mythical football ground such as Old Trafford.
"Manchester United are a huge club, a powerful machine and we are in for two very tough matches.
"We respect Manchester United but our aim is to become like them one day. Call me crazy, but I fear no opponents."
Olympiakos will host United in Athens in the first leg on February 25, then travel to Old Trafford to try and seal a quarter-final place two weeks later.