According to the Norwegian newspaper Dagbladet, Danish police fear that Møll may have fled Denmark and may currently be on the loose in Sweden or Norway.
Møll is described as a violent and dangerous repeat offender and the public are urged to be vigilant.
His modus operandi is the kidnap and rape of small girls. The Sankt Hans clinic in Roskilde where he was being held added that the medicine he takes to counter his compulsive behaviour will no longer be effective.
Møll has a long list of convictions for attacks against small girls and is said to be particularly devious and creative in his crimes.
He has managed to escape detention on several previous occasions and was last found in Oslo in possession of a fake passport, according to website E24.
The Swedish National Police Board told news agency TT on Sunday that they have no current information that the man may be in Sweden.