The Swans won 3-1 in the Capital One Cup in October and also earned a draw in their Premier League game with Brendan Rodgers' men.
The Swans sit a point above Liverpool in the league table, and they will face a Reds side which has already lost twice this week - to West Brom in domestic action on Monday and to Zenit St Petersburg in the Europa League on Thursday.
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."
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.
"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."