The coach of the Greek club believes his players can match the Red Devils when they clash in 2014 but acknowledged the tough task ahead.
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.