Wigan remain the Premier League bottom three, although victory over the Swans will take the Lancashire team out of the drop zone.
The Latics are also preparing for next Saturday's FA Cup final against Manchester City, but Laudrup does not expect the Wembley showpiece to be a distraction.
Laudrup said: "It will be a very hard game. I know they have the cup final coming up on the weekend, but we are talking about a team fighting for their football life.
"They will have been looking at the fixtures knowing they have two games left at home and they have Arsenal away.
"They know getting something out of the Arsenal game will be difficult. Roberto Martinez is like every manager, he will be looking at the numbers and he will want six points from their two home games and hope it is enough.
"They will come at us with everything they have."
Wigan's hopes of claiming a vital victory will have doubtlessly been boosted by Swansea's seven-game winless streak and the absence of top scorer Michu due to the hamstring injury he suffered in the weekend draw with Manchester City.
The Swans have little left to play for, but Laudrup does not expect any lack of effort from his players, whose performances he has praised despite recent results.
He said: "I will be putting out a strong team, Michu is injured so he cannot play but I will not be doing anyone any favours.
"Everyone wants to win games. Before our match against Manchester City, I watched Hull play Cardiff. Cardiff had already won the league but they went for it 100 per cent and this is what the game is all about. Even if you are safe you cannot relax."
Martinez is widely credited with establishing the passing philosophy which has become Swansea's hallmarks during their climb to the Premier League.
A handful of Swansea's current squad, including Ashley Williams, Leon Britton and Angel Rangel, all played under Martinez in south Wales, but Laudrup does not expect sentiment to play any part in proceedings, despite Wigan's precarious position.
He said: "They will not be down if we win. If we win they can still get to 41 points. They have three games to go and there are still plenty of teams that can go down."