The Latics' can draw inspiration from their 1-0 victory over United in April while Martinez also hopes his side can build on Saturday's success at Aston Villa.
"United is one of the hardest games that you're going to have in this league," he said. "They've set the pace in this year's competition, they've got seven points difference already to the champions, which is an incredible start.
"We're playing at home and we need to make sure we take advantage of that. If we are perfect and perform in the manner that we can do then we can challenge for three points against Manchester United.
"Last April we were in such a desperate need of points that we could only focus on ourselves and we did that.
"Obviously looking at the rest of the history, the stats are very bleak because it shows you we're playing one of the best teams in the world.
"But the result and performance against Aston Villa has given us a real sense of confidence in ourselves and this is an opportunity to show what we can do."