Anne-Elisabeth Falkevik Hagen, 68, has been missing since October 31, chief investigator Tommy Broeske said on Wednesday, with police saying she was abducted "against her will".
"The family chose to follow the police advice", Svein Holden told reporters.
The paper reported that it appeared the 68-year-old had been abducted from her bathroom of her home in Lorenskog and that there had been "limited dialogue" with her captors over the internet.
Police work outside of the house of of Norwegian multi-millionaire Tom Hagen in Fjellhamar East of Oslo
Authorities said the suspected kidnappers left a note in the couple's house, near the capital Oslo, detailing the fatal consequences if he refused to pay the demanded money in the form of the cryptocurrencies.
The newspaper reported that the note said Ms Falkevik Hagen would be killed if police were involved.
He is number 172 on a list of Norway's wealthiest people published by the financial magazine Kapital, with a fortune that amounted to almost 1.7 billion kroner ($200 million) in 2018, according to Norwegian news agency NTB.
Mr Hagen, who is Norway's 172nd richest man and made his fortune in real estate and the energy sector.
Police believe she disappeared from the couple's home, some 50 kilometers (30 miles) from the Swedish border. "If we do, they are prepared to start a process that could lead to her return", Holden said.
The ransom demands €9 million payable in privacy coin Monero, which would account for 1% of the coin's total market cap.
Hagen's wife disappeared suddenly from the family's Lørenskog home on October 31st, and hasn't been seen since.
Broske added during an appeal for help to the public: 'A ransom demand and serious threats have been issued.
'We need information, and that is why we now go out into the media.
Such events are extremely rare in the Scandinavian country, which enjoys a generally low crime rate. Broeske said they were working with Europol and Interpol on the case.