The reigning champions are on their worst run of form since 2001, having lost their last three games in a row, and face who side that knocked them out of the FA Cup
David Moyes's side are still seeking a first victory in 2014, having lost each of the three games they have played in January thus far.
One of those defeats came against Swansea in the FA Cup on January 5, when Wilfried Bony's late header secured a maiden win at Old Trafford for the Welsh club and progression to the fourth round.
Although United have now lost four of their last six home matches in all competitions, Swansea manager Laudrup expects a stiff test in the rematch as the reigning Premier League champions seek to respond to criticism.
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"I think it will be more difficult than last week. I expect them to come at us and they have to win this game.
"We have to be ready for that because we know it will be tough."
United currently sit seventh in the English top flight, five points adrift of fourth-placed Liverpool and 11 behind leaders Arsenal.
A 2-1 defeat at Sunderland on Tuesday in the first leg of a Capital One Cup semi-final left Moyes frustrated, although he is hopeful that his men can recover.
"I can sense in the dressing room that there's an urge to fight our current position," the Scot told United's official website.
Wayne Rooney could return to the United squad as the club continue to manage his groin problem but Robin van Persie is still unavailable with a thigh injury.
Jonny Evans (knock) and Phil Jones (knee) are in contention but Nani (hamstring) and Marouane Fellaini (wrist) are definitely out.
Swansea's injury crisis is slowly beginning to diminish, although Pablo Hernandez (hamstring), Roland Lamah (abductor), Michel Vorm (knee) and Michu (ankle) remain on the sidelines.