The Dane has been linked with some of Europe's top clubs after leading the Welsh club to the Capital One Cup during his first season in England.
Wieghorst is currently assistant manager at the Liberty Stadium, and Laudrup believes that the former Celtic player has the skills to take on the manager's job.
"I certainly believe he can be manager here," Laudrup told Wales Online.
"He has experience from Scottish football and is familiar with [English football]. He has shown ability in Denmark, both with FC Nordsjaelland and the under-21 national team."
Swansea are currently eighth in the Premier League table.