The Red Devils will be eager to keep their unbeaten run of 10 games in all competitions going against Jurgen Klopp's men, but Mourinho admits it will be a difficult Premier League encounter.
"I like to play against the best teams, I like to play against the best clubs and I like to play at the best stadiums - the stadiums with more history," Mourinho told Sky Sports.
"And you are right, at Anfield I've had great moments and I've had bad moments. They have had happiness against me, they have had very sad moments against me.
"(Now) if they respect me as much as I respect them, we are going to have another one of those matches."
United enjoy a seven-point lead over Liverpool in the league standings and Mourinho believes that even though it's not a battle for the title yet, it's still a crucial game against a top side.
"It's for three points, not four," he added. "Maybe if we were in a moment of the season where it was a duel between two teams it would mean more but it's not the case.
"At the same time, in these kinds of matches, every single moment plays a part. We are playing against a good team with very good players."