The Midlands club travel to the Liberty Stadium on New Year's Day in disarray after a run of three heavy defeats against Chelsea, Tottenham and Wigan.
Villa have conceded 15 goals and scored none during that sequence, sliding to within a point of the relegation zone.
Paul Lambert's side had been unbeaten in six games before their nightmare festive run, and had picked up handsome wins at Norwich in the Capital One Cup and Liverpool in the league.
But Laudrup, who is waiting on the fitness of Michu ahead of the meeting with the Villans, believes Lambert can turn their fortunes around, and highlighted Swansea's own dip in form in September as a sign they can recover.
He said: "I think Villa are a fantastic example of how quick things can change.
"They were going well, in the Capital One Cup they had a fantastic game at Norwich winning 4-1 - Norwich's first defeat in nine or 10 games.
"Villa then go to Anfield and have a great performance and win 3-1, now they have lost three in a row - 15 goals against, zero scored.
"We did that, we had a fantastic start to the season then lost three games, then we had a game against Crawley in the cup when we scored the winner in the 91st minute.
"Newcastle have been the same. I could pick seven or eight teams who have suddenly gone down but then they can come up again."
While Villa are nervously looking over their shoulder, Swansea are enjoying the relative comfort of a place in the top half of the Barclays Premier League table.
Victory over Fulham on Saturday moved the Swans on to 28 points, putting them five points better off than after the same number of games last season.
But midfielder Jonathan de Guzman, who grabbed the clinching goal at Craven Cottage, has warned there must be no complacency from Laudrup's men until they have secured at least one more season in the top flight.
"It's always important to keep that distance from you and the teams near the bottom of the table so that's why the game against Villa is important," he said.
"It's why winning at Fulham was a good win for us, especially when not playing the best football.
"The mark is 40 points and we have to keep it real and get those points on board and stay away from danger.
"We've been doing well and we can be happy at the end of the year to be where we are."
The Welsh club have lost all three fixtures in which they have faced a side managed by Lambert in the Premier League, including the 2-0 reverse at Villa Park earlier in the campaign.
De Guzman said: "We fell apart in the second half there. They scored a cracking goal against the run of play and we tried to pull through and play our game, but they made it 2-0 and that was it over, so we want our revenge in the home game."