Manuel Pellegrini's championship favourites go to Wales on the back of 10 wins in 11 games - one of which was a 3-0 victory over Swansea at the Etihad.
But Swansea had their chances in Manchester, Jonathan de Guzman missing the best of them with the score 1-0, and Laudrup reckons a shock result is possible if his side can avoid a repeat of that wastefulness.
He said: "We played them a month ago and played very well in the first half. We didn't take our chances, and in the end they beat us 3-0 because they have so much quality.
"But what makes this sport so unique is that, even when you look at their squad and see a player who has the same value as the whole of your team, you still have a chance.
"If we can play like we did last time, as well as take our chances, I really think we have a chance.
"But we have to take our chances when we get them, because you will not get seven clear goal chances against a team like City."
Swansea go into the New Year 11th in the table, but Laudrup knows a five-point cushion on the bottom three leaves no room for complacency.
"We are 11th but everyone is within a few points," he said. "I know there are a couple of teams below with 14 or 15 points but Sunderland have shown they can get out of it, West Ham can do it and Crystal Palace have done really well in the last month or so.
"So you always have to have respect for the number of points teams have. If you were to say relegation is none of my concern then you are very arrogant. None of the bottom 11 teams can say that."