United are desperate to halt a run of three successive defeats which has seen them crash out of the FA Cup, drop to seventh in the table and slip-up 2-1 in their Capital One Cup semi-final first leg at the Stadium of Light.
After chalking up six wins in a row, David Moyes' side suffered three straight losses - against Tottenham, Swansea and Sunderland - for the first time in 13 years to spark talk of a mini crisis at the club.
Swansea, who ended their interest in the FA Cup last weekend, return to Old Trafford on Saturday hoping to inflict a fourth successive defeat on United for the first time since November 1961.
But Laudrup has warned his team to expect a backlash, saying: "Manchester United will come out and have a real go at us.
"This is a game they want to win, they have to win this game and we must be ready for that.
"I don't think the United players like what they are reading and what they are hearing at the moment about these negative records so I know this will be a very tough game for us.
"But football can change in a very short space of time. If they beat us, win their next game then beat Sunderland 1-0 in their second leg, suddenly they're back near the top four in the league and in a final at Wembley."
Despite expectations of the tough task ahead, Laudrup, who travels north without the services of injured duo Jonathan de Guzman (calf) and Dwight Tiendalli (hamstring), is refusing to rule out a second successive Manchester success for his side.
"We have shown it's possible to win there," he said. "In recent games we have played with a lot of confidence, and we just needed that win.
"Sometimes a victory comes when you least expect it and that came at Old Trafford.
"On one hand we know it is possible and now we have confidence going there. However, I think it will be a more difficult game than the one we had there last week."
Watch Manchester United v Swansea live from 5.00pm this Saturday on Sky Sports 1HD and Sky Sports 3D