The Gunners are off the pace in the Premier League, out of the Carling Cup and facing a tough Champions League clash with AC Milan, so Laudrup thinks they will see the FA Cup as their best chance of a trophy this term.
"I think there is pressure on them," said Laudrup. "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, so 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 have beaten Arsenal twice since returning to the top flight but Laudrup added: "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 back at right back. I expect them to put out their strongest team."
Big spending off the menu
Laudrup says he may look to strengthen his squad during the transfer window but is not expecting to make any expensive acquisitions.
"I don't think we will spend a lot of money," he said. "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 and I don't think we will spend that much."