Crown Princess Mette-Marit was a single mother to Mr Høiby when she met her husband Prince Haakon.
Mr Høiby, 27, has been charged with causing damage and bodily harm since the incident, for which he faces up to one year in prison.
According to Se og Hør, the victim had been in a “relationship” with Mr Høiby at the time of the attack, which took place on Aug 4 in Oslo.
The woman, said to be in her 20s, made Mr Høiby leave the apartment after the attack and called the police. They took her to a hospital where she was diagnosed with a concussion.
A source told Se og Hør that police suspect Mr Høiby had plunged the knife into the wall during the alleged attack and were seeking forensic evidence to confirm this.
Two other sources told the magazine that police had audio recordings of Mr Høiby “threatening to set fire to and burn the girl’s clothes and belongings”.
Police are also attempting to put together a “minute by minute” reconstruction of the attack, the magazine said.
The Telegraph approached the Royal House of Norway for comment but did not immediately receive a response.
Mr Høiby has never held a royal title. Growing up, he made public appearances with his mother, stepfather and siblings.
He stepped back from public life in 2017 aged 20 in pursuit of privacy.
Haakon Magnus, the Crown Prince of Norway, has previously said of the case: “It’s a serious matter when police are involved like this...at the same time, it would not be right for me to comment on it at this time.”
Oyvind Bratlien, Mr Høiby’s lawyer, told Se og Hør: “It is important that the process is allowed to take its course in the right way, and that the media respects my client’s need for privacy and tranquillity. The police must be allowed to do their job without the media deciding the facts and culpability.”