The Gunners' head to south Wales with their Premier League title aspirations all but over, a testing Champions League last-16 tie against AC Milan to come and having already exited the Capital One Cup after their quarter-final humbling at Bradford.
That would appear to leave the FA Cup as the north London club's best hope of picking up their first silverware since winning the same competition in 2005, making the trip to the Liberty Stadium a crucial fixture in the context of Arsenal's season.
Laudrup said: "I think there is pressure on them. For them when you are a top team you are obliged to at least compete until the end to win things.
"There can only be one winner in all competitions and two teams in a final and they are expected to at least be in the semi-finals there is more pressure at this stage on Arsenal than on Swansea, that is obvious.
"Looking from the outside, Arsenal are a big club and big clubs are obliged to play in finals.
"They played a (League Cup) final the year before last and they lost, but it is many years since they won a trophy, which is why they will come here with the best team they can put on the pitch and that is what I have to look forward to."