Kagawa is hoping to return to make his sixth appearance in Europe this season, having not featured for the Reds at all since the Capital One Cup semi-final second leg against Sunderland on 22 January.
The Japanese playmaker is keen for United to go further in the Champions League than in his first season, when Real Madrid ended the Reds' hopes at the last 16 stage.
But he expects a tough encounter at the Karaiskakis Stadium, where Olympiacos have lost just once in 19 home games this season in all competitions – that solitary defeat was at the hands of runaway Group C winners Paris Saint-Germain.
"When you get to this stage in the competition you can't afford any slip-ups or you're out," Kagawa told ManUtd.com. "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.
"Our Champions League campaign ended at the last 16 stage last season, so we want to go further this time.
"Olympiacos 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."