Victory for the Greek side, who come to Old Trafford with a 2-0 lead from the first leg three weeks ago, would end manager David Moyes' hopes of landing any silverware in his first season at United. (Agencies)
"I know the situation at Manchester United but that has nothing to do with us," Michel told reporters on the eve of Wednesday's match.
"I have sympathy with every coach because I am a coach myself. David Moyes has obviously been working hard and sometimes results go against you, but he is an opponent, not an enemy and I feel for him.
"But we will not sit back and defend deeply. We are playing against a very good team who will be even more motivated and stronger than they were in Athens and they will have their crowd behind them.
"But we will go for the goal that we need to give ourselves a decent chance. We cannot sit back and defend a 2-0 lead."
If Olympiakos do score they will break new ground having failed to net in their two previous matches at Old Trafford - a 3-0 defeat in the Champions League group stage in 2001 followed by a 4-0 loss in their section the following season.
United have only conceded one goal in five home matches against Greek teams in Europe from a free-kick scored by Giorgios Karagounis when United beat Panathinaikos 3-1 in a second round group stage match in November 2000.
Olympiakos scored their first ever goals against United when they won the first leg with strikes from Alejandro Dominguez and Joel Campbell and are now on the verge of knocking the Premier League champions out of Europe.
If they do that, United's hopes of winning a trophy this season will be over as they were eliminated in the League Cup semi-finals, fell in the FA Cup third round and are languishing in seventh place in the league.
United's woes matter little to Olympiakos captain Avraam Papadopoulos, who is trying to guide his team to the last eight for the first time since 1999.
"We cannot sit back and defend, that's for sure. We are pleased we have made the last 16, but we now want to prove we can do better than that and reach the last eight to show we have moved up a level when it comes to European competition," Papadopoulos told reporters.
"We know that at 2-0 the tie is not over but we are in a very good position to win it."
There was uncertainty if Olympiakos striker Javier Saviola would be fit to start the match as the Argentine did not take part in the full training session at Old Trafford on Tuesday.
Asked if Saviola would be fit to play on Wednesday, Michel avoided the issue by just smiling and saying: "He is very well thank you."
Victory for the Greek side, who come to Old Trafford with a 2-0 lead from the first leg three weeks ago, would end manager David Moyes' hopes of landing any silverware in his first season at United.