The Swans enjoyed a 3-1 success over the Reds when they met on Merseyside in the Capital One Cup in October, putting one over on former manager Brendan Rodgers.
The Welsh club also claimed a point in the league meeting at the Liberty Stadium, and sit above Rodgers' team in the table after the Reds lost to West Brom on Monday.
Liverpool followed that reverse against the Baggies with Thursday's Europa League defeat to Zenit St Petersburg in Russia.
But Laudrup has seen signs Liverpool are becoming increasingly confident in Rodgers' methods and expects them to be a tougher proposition this time around.
"They are better now than when we played the cup game," he said.
"They have a couple of new players, we saw they have brought in (Daniel) Sturridge to play with (Luis) Suarez, and they have had more time with the new manager and understand how he works.
"I have watched them over the last five or six games before they played West Brom and they are getting better all the time."
Last weekend's win over QPR moved Swansea onto 37 points, putting them just a victory away from the oft-stated survival target of 40.
As a result Laudrup feels his side can travel to Anfield with no pressure on their shoulders, after enjoying a warm-weather training camp in Dubai this week.
But the Dane expects the high standard of Swansea's away performances, which have resulted in wins at the likes of Arsenal, Chelsea and Newcastle so far this season, to be maintained.
"Winning against QPR and with the points we have, we can go there with no pressure at all," he said.
"That does not mean we give the game away, we always want to be competitive, but the pressure will be on them, they are a team who have to go into Europe and they are strong.
"Anfield is one of those grounds where you can never expect to get anything, like at Old Trafford or the Etihad Stadium. I know we have had results at some of these grounds like the Emirates and Stamford Bridge, but normally they are huge favourites."