The hosts have lost just once at home all season, a 4-1 defeat to PSG in the Champions League in September, and currently lead the Greek Super League by 20 points.
In stark contrast, United are a distant sixth in the Premier League but topped their qualifying group and are yet to taste defeat in Europe this season.
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"The away leg is very important - we need to get a good result there. We have a lot of experienced players in our squad who will hopefully help us to achieve that."
The Japan international also says that his team are determined to improve on last season, when they were dumped out of the tournament at this stage by Real Madrid.
"Our Champions League campaign ended at the last-16 stage last season so we want to go further this time," he added.
"Olympiakos are a good team and there are no easy games in this competition - we all know that - so we have to prepare as well as we can."