If St Gallen fail to beat Kuban Krasnodar in the early game, then the Swans will be through before kickoff at the Liberty Stadium.
However, Laudrup said that they will be going for the result against Los Che regardless of what happens in Russia.
"We still need something, depending on what happens in the early game, but we have the chance to go into the next stage - and the sooner, the better," the Dane told The Mirror. "If we can do it on Thursday then we know we will move on.
"For less than three months we can think exclusively about the Premier League, which is our main thing. We have 12 games in 43 days coming up and there's a huge difference between going there knowing we have already qualified and playing for first or second and playing to be in or out.
"The last thing I want is to have to go to St Gallen on December 12 with three, four or five degrees below zero and play for qualification in 90 minutes."
Swansea travel to Manchester City in the Premier League on Sunday.