The Primera Division side are the top seed in the competition, and are the favourites to top Group A, which also includes Kuban Krasnodar and St Gallen.
But Los Che have endured a difficult start to their campaign, and Sunday's 3-1 defeat at Real Betis leaves them 16th in the table, building the scrutiny on new boss Miroslav Djukic, who succeeded Ernesto Valverde in June.
Valencia have traditionally been the closest rivals to Real Madrid and Barcelona's dominance of the Spanish game.
They were Champions League runners-up in 2000 and 2001, with former Liverpool manager Rafael Benitez then guiding them to two La Liga titles and a UEFA Cup win during his tenure.
Laudrup, does not feel the current squad lives up to those standards, and believes his Swans have a chance of getting a good result on Thursday night.
He said: "They have been the third team in Spain for many years. Maybe at this moment Atletico Madrid are just above them.
"Having said that, they have had a very rough start. They have a new manager and they have sold a couple of their top players, like Roberto Soldado to Tottenham.
"They have had only one win in four games and on Sunday they play Sevilla, so it's a difficult moment for them. We have to do our best and, if we do that, I think we have a good chance."
He added: "The Valencia fans have been used to seeing great players and great teams at their club.
"They always want the best and they ask for that. They demand it from the players and the manager, that they are up there competing with Barcelona and Real Madrid.
"Let's see how they react to where they are now, because in their minds Valencia are way beyond Swansea, even though we play in the Premier League.
"With all these small things and the moment they are in, let's see if we can take advantage."
Swansea have reached Laudrup's minimum requirement for their European adventure by reaching the group stage, and the Dane is glad the supporters have an opening fixture to saviour in a country where he is revered for his playing exploits with Barca and Real.
He said: "It will be a huge experience. It's a great stadium. It is not new but it is big and I think for the fans, knowing what this club have achieved, it is great. Now we are playing them it has to be a great evening.
"I always enjoyed great football games here, whether it was with Barca or Madrid.
"Valencia always want to play good football, so I think this will be a very good game between two sides who play possession football."
- Sports & Recreation
- Real Madrid
- Ernesto Valverde
- Real Betis