Laudrup took Getafe to the Copa del Rey final in 2008 when he worked in Spain and he now wants a Wembley appearance with Swansea who have never previously got this far in the competition in their 100-year history.
He said: "The downside with Getafe was we lost the final, but I still remember when we started in the first round all the way through to the final.
"It was very special and we also got to the Europa League quarter-finals.
"It was a fantastic year, though obviously we had to keep our eyes on the league and you have to manage that, that's the difficult part.
"That's something we could have to manage in January, but there is the possibility to maybe go and play in a final and win a trophy.
"When you are a smaller club when do you ever get the chance to play for a trophy?
"Being in mid-table or avoiding relegation is great, but it is a special feeling to win a trophy and we can do it with a cup.
"I have been to Wembley as a player, and been to finals as a manager and it's special.
"Cups are so special, you can win, lose or draw in the league, but in the cup it is one or the other - you go on or you're out."
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar