Laudrup will lead his side out against League Two Bradford in the Capital One Cup final, having previously played a part in two historic triumphs at the home of English football.
In 1983, Laudrup was part of the first Denmark side to taste victory over England, thanks to Allan Simonsen's penalty.
The Dane also famously featured for Barcelona's 'Dream Team' when they recorded the Catalan club's first European Cup success against Sampdoria in 1992.
A Swansea victory on Sunday would see the Welsh club secure the first major trophy in their centenary season, and Laudrup said: "I had two very good days at Wembley, although that was the old ground.
"In 1983 Denmark won 1-0 against England with a penalty from Allan Simonsen and we qualified instead of England for the European Championship in 1984.
"In May 1992, in the final of the European Cup, we (Barcelona) won after extra-time 1-0 against Sampdoria, who had Roberto Mancini and Gianluca Vialli on their side.
"They were two huge results and I hope Sunday will be the third."
Laudrup has enjoyed a superb first season in charge of the Swans, guiding them to a position in the top half of the Premier League table as well as Sunday's final.
Their performances have seen Laudrup linked with jobs at Real Madrid, Chelsea and Manchester City and he is set to discuss an extension to his deal at the Liberty Stadium.
Laudrup places his managerial abilities down to learning from those he played under, and there were none as influential as the man in charge for Barcelona's night of Wembley glory: Johan Cruyff.
"On the pitch everyone knows my five years with Cruyff in Barcelona were great years, there are a lot of things from the training I did with him that I am using now," he said.
"There are also elements from Giovanni Trapattoni while I was in Italy and (former Denmark boss) Sepp Piontek.
"Those are the three I mention when people ask who had the most influence on my career - so we have a German, an Italian and a Dutchman who was from the school of 'Total Football' and was one of the top five players ever.
"They were three very different personalities, and three very different ways of seeing the game, but they had a big impact on me."
@highasballs , beating England at Wembley to quality for the European Championships is a pretty big thing- fictionalemu