"The reason for us to go public with this case now is that, despite a broad and extensive investigation, we need more information", chief police investigator Tommy Broeske told a news conference.
Investigators refused to confirm the amount but said they advised the family not to pay the purported kidnappers.
Police have been investigating the case discreetly for several weeks but decided to make it public in the hope that someone would come forward with information, Broske said.
Married to a businessman who made his fortune in real estate and the energy sector, 68-year-old Anne-Elisabeth Falkevik disappeared on October 31, the Verdens Gang newspaper said.
Sources have now indicated that a written message was found in the Hagen house, which demanded a $10 million ransom be paid entirely with the privacy-focused cryptocurrency Monero.More news: Fox News’ Shepard Smith Relentlessly Fact Checks Donald Trump’s Border Wall Address!
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It has also been reported that there had been limited contact between police and the suspects with the only communication sent through encrypted digital platforms.
The ransom demands €9 million payable in privacy coin Monero, which would account for 1% of the coin's total market cap.
As a result, investigators on the case are still left with "no suspects", despite having assistance from Interpol and Europol, and have Hagen's wealth behind them.
News of the months-long disappearance was first reported by the newspaper Aftenposten early on Wednesday, which said it had known about the case for some time but had chosen not to publish details to protect Mrs Hagen.
Police said the woman disappeared about 31 miles from the Swedish border.
The cautious nature of the remarks could be an indication that police have not received proof that Hagen was indeed being held by the people demanding the ransom. Norwegian police have also engaged worldwide counterparts in Interpol and Europol as part of the probe.