United are three points clear of the 2019-20 champions at the top of the Premier League table but Solskjaer believes winning on Sunday would be "an upset" because Jurgen Klopp's team have not lost a home game in the league since April 2017.
"If you look at the last few seasons, it would be an upset, it would be a shock," Solskjaer told a news conference on Friday.
"We're looking forward to the game and hopefully we can cause that upset.
"I'd rather be on top and have the points than chasing but we are the challengers, the hunters, chasing the champions, over the course of a long season.
"They've got the cup, they are the champions, the ones everyone would like to beat and my players are the same."
United have not lost away from home in the league since a 2-0 defeat at Liverpool almost a year ago.
They have not won at Anfield since 2016 but Solskjaer said the task will be made easier this time because they won't have to deal with the hostile reception from Liverpool fans with the game being played behind closed doors.
"I think football and the results in general have shown how important the fans are," Solskjaer aded.
"We've not lost away since Anfield, that's a year. Compared to a year ago it's a bit of an advantage this time. To be at home with your fans is the best feeling for a player. It's not just a cliche, you need your supporters."
Martial was forced off with a hamstring injury but he will be given time to prove his fitness.
"I'm going to give everyone another day," Solskjaer said.
"Anthony is not out of it, the only ones certainly out are Brandon [Williams] and Phil Jones, they're the two that definitely can't make the game. A couple of others are maybe doubts but we're hoping. Fingers crossed."