The man's body was discovered at around 7.30am, with police immediately cordoning off the area under the bridge where he was found which is by the town's railway station.
The region is currently hosting thousands of international athletes and sports fans who are in Falun to watch the Nordic World Ski Championships (officially known as the Audi FIS Ski World Cup).
"We can't be 100 percent sure of the man's identity but we have a theory that he is a 55 year old who is not from the local area," Stefan Dangardt, a spokesperson for the region's police force told The Local on Tuesday afternoon.
Asked if the man could have been a skiing enthusiast who was visiting Falun, he responded: "Absolutely, that is certainly a possibility we are looking into".
He said that around ten police officers were currently working on the case and that an autopsy was being carried out on the man's body.
Forensic teams remain underneath the bridge where the body was discovered.
The Ski World Cup takes place over twelve days and includes cross-country skiing, ski jumping, combined and team events.
On Tuesday afternoon, one of Sweden's biggest stars Charlotte Kalla won gold in the 10km individual ladies' race.
Sweden's Charlotte Kalla who was competing on Tuesday. Photo: TT