Her partner raised the alarm in the early hours of Friday when she failed to return from the Nautilus vessel.
Madsen escaped from the submarine as it sank and was rescued by a private boat.
A boater who helped search a private submarine that sank off Denmark says he saw inventor Peter Madsen Kristian standing in the vessel's tower while it was still afloat.
The submarine was located Friday at a depth of seven meters (22-feet), south of Copenhagen.
Nautilus, named after the ship from the classic science fiction novel Twenty Thousand Leagues Under the Sea, was built by Mr Madsen after raising $200,000 (£154,000) online.
When asked about the whereabouts of Wall, he claimed that he dropped her off near a restaurant on Refshaleon Island in Copenhagen harbor on Thursday evening, and then gave his own account of the sinking.
Madsen said "a minor problem with a ballast tank" a compartment that holds water to provide stability "turned into a major issue" that ultimately caused the submarine to sink.
The police in Sweden said they had tried without success to contact her by phone and that her family had not heard from her. "But I guess that was pretty good, because I otherwise still would have been down there".
"He told us that the journalist who also had been on board had been dropped off Thursday evening", navy spokesman Anders Damgaard said. The navy says that the 40-ton, almost 18-meter-long (60-foot-long) submarine with at least two people on board had been "found sailing" south of Copenhagen. They were hoping to tow it to port on Saturday and open it then, the statement said. RML Spacelab is seeking to send people into space and is developing a rocket, floating launch pad and astronaut testing machine among other projects, the site says. "I design and manufacture non-commercial extreme machines, employing teams of volunteering engineers and technicians to challenge the ordinary".
Ms Wall had been writing about Madsen for a story and is believed to have set sail with him from Refshale Island at 7pm on Thursday.
"He then climbed down inside the submarine and there was then some kind of air flow coming up and the submarine started to sink", Isbak told The Associated Press. The Navy said that the sub had been spotted sailing but then sank shortly afterward.