Danish prosecutors have said they will seek a murder charge against the do-it-yourself submarine inventor who was last seen with Swedish journalist Kim Wall before her headless torso was found floating off Denmark.

"At latest on September 5, we will try to hold [Peter Madsen] in custody on a murder charge ... after her [dismembered] body was found," special prosecutor Jakob Buch-Jepsen told AFP this afternoon.

The 46-year-old inventor has been held in formal custody since 12 August on suspicion of "negligent manslaughter", in a case that has shocked and intrigued people around the world.

Kim Wall was last seen alive on 10 August

Prosecutors have until 5 September to request an extension of his custody.

Mr Madsen, who has denied the allegations against him, has insisted Ms Wall died in an accident on board and that he dumped the body in the water at an undefined location in Koge Bay, south of Copenhagen.

Prosecutors said they plan to seek a murder charge after the recovery of the Ms Wall's body, which investigators say was "deliberately" mutilated and weighted down with a metal object.

Ms Wall, a freelance journalist who has reported for The New York Times and The Guardian, was last seen onboard Mr Madsen's submarine on 10 August to interview him for a feature story.

Her boyfriend reported her missing a day later. The same day, Mr Madsen was rescued from waters between Denmark and Sweden shortly before his submarine sank.

Investigators recovered and searched the sunken submarine, which police believe Mr Madsen sank intentionally. 

The cause of death and motive remain unknown.