The south Wales side claimed their first ever win at the famous old stadium on Sunday when Wilfried Bony's last-minute header gave them a 2-1 victory in their FA Cup third-round tie.
Under normal circumstances, a reaction would be expected from United, although given the recent form of David Moyes' side, nothing can be taken for granted.
However, it is not the failings of United that mean Laudrup is happy to take on a re-match. It is those of his own team.
"I am happy we play here again next week because if we had played against one of the smaller clubs [in the third round of the cup], in five or six days there is a chance we could underperform," he said.
"Sometimes when the smaller teams have a great result, everyone is talking about how historic it is - last year we won 2-0 at Arsenal and the media all came down to Swansea to do interviews - and the next game we played Norwich and were 3-0 down at half-time.
"We woke up and only lost 4-3 but that tells you how it is."
Nevertheless, as one of five teams who have won at Old Trafford this season, and four out of the last six visitors, Swansea will head north will a feeling of huge optimism.
Not that Laudrup regards United as a soft touch.
"I've been asked if that special thing about Old Trafford has changed because four teams had won here [before us]," he said.
"But the reason why some stadiums are very special - Old Trafford, Bernabeu, Camp Nou and so on - it's because of the history of the clubs, not because of what has happened in one, two or three seasons.
"Yes, it is a little rare when you see teams who haven't won for five, 10, 15 or 25 years win here but it doesn't mean it's something that can happen every day.
"It may be the next time Swansea win at Old Trafford will be in 15 years.
"If you play Manchester United ten times or Chelsea 10 times away, maybe you win one or two and have a couple of draws but lose the rest.
"But because something happened one year doesn't take away the history of the club - Old Trafford will always be special for every player who comes here and tries to get something."