The Gunners' head to south Wales with their Premier League title aspirations all but over, a testing Champions League last-16 tie against Bayern Munich 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."
Swansea's record against Arsenal since gaining promotion to the Premier League has been good.
The south Wales club secured a thrilling 3-2 victory at the Liberty Stadium almost a year ago, and came out on top 2-0 at the Emirates earlier this season.
But Laudrup feels those successes will count for nothing come Sunday lunchtime.
He said: "Those games mean nothing, this is a new game and it will be a different team we face.
"The players will be the same but they have changed with Theo Walcott playing as a centre forward and Bacary Sagna is back at right back, and I expect them to put out their strongest team."
With the January transfer window now open, Laudrup is keen to add to his squad and maintain Swansea's excellent start to the season, which sees them lie ninth in the Premier League table and looking forward to the first leg of Capital One Cup semi-final against Chelsea on Wednesday.
But the Dane, who has been linked with an £8million move for Celta Vigo forward Iago Aspas, suggested he will not break the club transfer record of £5.55million this month.
He said: "I don't think we will spend a lot of money, it is easy to spend money but I would rather spend it well.
"This club is one of the few with black numbers at the bottom of the balance sheet and it is not often you see that.
"It is not about spending money just to spend, we have to do well but I don't think we will spend that much."