On August 12 Madsen was remanded in custody for 24 days on suspicion of manslaughter.
"We believe he is telling the truth when he says she died in the submarine", said a spokesperson at the Copenhagen Police to TT.
Wall's body has not yet been found. Madsen said that he "buried" Wall's body at sea in the Bay of Koge, south of the Danish capital.
On the evening of August 10, Madsen and Wall went on a submarine tour around Copenhagen. Madsen was rescued, but Wall has remained missing ever since.
Police have previously stated it appeared the 40-foot vessel, known as UC3 Nautilus, had been deliberately sunk.
Danish broadcaster TV2 showed images of Madsen as he was being interrogated by police after his rescue. He was shortly afterward arrested by police.
When a journalist asked Madsen what about contact information he had for the missing journalist, he responded: "Only that her name is Kim".
"My client is relieved that these observations have been revealed".
Citing Copenhagen police, the BBC reported that the search for Wall's body is still ongoing. "As the investigation of the case is still covered by 'closed doors, ' no further information can be given".
Wall's friends told local news media that she had already signed a lease for a studio apartment in Beijing, as she was planning on moving to China with her boyfriend.
Miss Wall was a world renowned writer who was a graduate of Columbia's Graduate School of Journalism and freelanced in NY and China.