The Swans have not beaten the Canaries since their promotion to the top flight in 2011, but would have fancied their chances of ending that sequence when Chris Hughton's men made a slow start to the season.
But Norwich have won three of their last five fixtures and now lie just two points behind Swansea after their 2-0 win at West Brom last weekend.
Swans' boss Laudrup admits it makes the trip to East Anglia more testing than it may have seemed a few weeks ago.
The Dane said: "Of course this is a tougher game than it would have been a month ago.
"Circumstances change. It's the same team, the same pitch, the same ball, but in a different moment and circumstance.
"If they beat us they go above us by a point. That's how it is, maybe a month ago or in a month's time it would be different, but we are not playing last month we are playing Sunday.
"Three or four weeks ago I watched them at home in a crucial game against West Ham.
"In the first half they were outplayed and could have been three or four nil down.
"Then in the second half they got a penalty and a great free-kick from Robert Snodgrass and went on to score a third goal.
"Since then in the last three games they have won two. Suddenly from being in a very difficult position they are right up there."
Sunday's game comes just three days after Swansea advanced to the last 32 of the Europa League despite losing 1-0 to St Gallen in Switzerland.
The hectic schedule caused by the 10 European games the Welsh club have played so far has seen Laudrup forced to constantly rotate his squad.
But he hopes, with a two-month gap until the knockout stages, his side can settle down and find some consistency.
"It is mission accomplished in Europe but now we have an important game on Sunday," said Laudrup.
"It will be the seventh game in 20 days with some players playing in four, five or six of those.
"But we have to get everything we can out of this game and then on Monday we can enjoy the Europa League draw and then park that competition until the end of February.
"After that we can think exclusively about the Premier League as from here to the next Europa League game there are 10 or 11 games in the league.
"It is always easier to focus on one competition, especially if you are not experienced in playing in Europe.
"This is the first time in the Europa League for us and we are only in mid-December but we've already had 10 games in this competition.
"That's a lot of games. Last year we thought we'd played a lot of games, but we've played more this year at a similar stage."
Source: PA
Source: PA