The investigation has been continuing since then, police said, but was given "a low profile" because "very serious threats have been made".
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".
Police refused to confirm the sum but said they had advised the family not to pay.
The abducted woman's husband is one of Norway's wealthiest men, with an estimated net-worth of $200 million dollars accumulated from the real-estate and energy markets. It is the country's first kidnap for crypto ransom.
Image Police believe the kidnap happened at the couple's house
The newspaper reported that the note said Ms Falkevik Hagen would be killed if police were involved.
Police wouldn't divulge the size of the demand.
A ransom of 9 million euros (roughly R144 million) has been demanded for Anne-Elisabeth Falkevik Hagen, who has been missing since October 31, according to Oslo daily VG.More news: Musk lays foundation of USD 7 billion Tesla plant in China
Tommy Broeske, a Police Inspector said that, at present, their goal is to find the missing woman "alive and reunite her with the family".
It remains unclear what the exact figure of the demanded ransom is, but local Norwegian media claim the kidnappers asked for more than $10 million.
On Wednesday morning, as Aftenposten published its report, police put a cordon around the couple's home.
"Our main theory is that the victim was kidnapped by unidentified perpetrators at her home" in Lorenskog, about 20 kilometers (12 miles) from Oslo, he said, adding that police have from the beginning examined several possible theories about her disappearance.More news: PG&E Reportedly Eyeing Breakup, Bankruptcy In Wake Of Multiple Devastating Wildfires
Norwegian police believe that the 68-year-old was taken from her home in Sloraveien, with forensics teams analysing traces of the kidnappers in the bathroom of Hagen's detached house.
Norwegian authorities are working together with Europol and Interpol on the case.More news: PM Imran congratulates India on historic Test series win in Australia