Laudrup's success this season in charge of the Swans has gained both plaudits and reported interest from some of Europe's biggest clubs.
The Dane believes that Wieghorst, who joined Swansea earlier this month as assistant manager at the Liberty Stadium, could be the ideal man to fill the breach if Laudrup does decide to move on at any point.
"I certainly believe he can be manager here," Laudrup told Sporten.dk.
"He has experience from Scottish football and is familiar with [English football].
"He has shown ability in Denmark, both with FC Nordsjaelland and the U-21 national team."
Wieghorst made over 150 league appearances in Scotland for both Dundee and Celtic, and played alongside Laudrup for Denmark.