David Moyes' men fell to a 2-1 home defeat to Tottenham in the Premier League on New Year's Day and are enduring their worst home league form for more than a decade.
United had won their previous six fixtures in all competitions and already have a victory over Michael Laudrup's men to their name this season, winning 4-1 at the Liberty Stadium on the opening day of the campaign.
The Premier League champions, who have not won the FA Cup since 2004, currently sit 11 points adrift of league leaders Arsenal, and the Scot may view this competition as a chance to snaffle some silverware in his first season in charge.
Moyes' side made it to the sixth round of last year's competition, losing 1-0 to Chelsea in a replay after the sides had drawn 2-2 in the initial encounter.
"We're trying to win all the competitions," he said in the build-up to the clash. "As far as I am concerned, we'll do everything we possibly can to try to get through.
"The cup is important to me, it always has been. I'm sure it's important to every club. The longer you stay in the competition the more important it becomes.
"If you're a club like Manchester United you want to be involved in all the trophy-winning opportunities, and to not win the FA Cup for 10 years is something that's a bit of a surprise."
For Swansea, this fixture marks the midway point of a Manchester triple header.
The men from Wales suffered a 3-2 home defeat to Manchester City on Wednesday, and face United for a second time in the Premier League next weekend.
They are currently on a run of seven matches without a win in all competitions, and two fixtures against United followed by the visit of Tottenham will not help their cause.
Swansea lost at this stage to Arsenal last year after a replay though their focus that time around was on their ultimately successful League Cup campaign.
United will be forced to do without Ashley Young (shoulder), while Phil Jones (knee), Rafael (groin), Marouane Fellaini (wrist) and Nani (hamstring) remain sidelined. Robin van Persie (groin and thigh) has returned to training but is unlikely to feature.
Pablo Hernandez suffered hamstring injury in Swansea's defeat to Manchester City, joining Michu (ankle), Michel Vorm (knee) and Nathan Dyer (ankle) in being ruled out of the clash.
