The Greek champions finished second in Group C behind Paris Saint-Germain and will now face the Red Devils for the fifth and sixth time in their history — and for the first time since 2002.
Michel's side has never tasted success against the English champions and the Spaniard is determined to spring a surprise.
"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 Feb. 25, then travel to Old Trafford to try and seal a quarterfinal place in March.