Madsen's defence lawyer Betina Hald told broadcaster TV2 that the inventor, who built the submarine at the centre of the case, had accepted Copenhagen City Court's decision Saturday to remand him in custody for 24 days.
Hald added that Madsen, 46, still denies the charges against him, but declined to make any further comment.
“I met with my client on Sunday and we have decided not to say any more,” she told TV2.
Swedish tabloid Aftonbladet reported on Monday that a freight ship almost collided with Madsen's Nautilus sub as it sailed in the Öresund waters off Copenhagen late on Thursday.
The near-collision is reported to have taken place just over two hours before the submarine was reported missing.
“There was very nearly a collision,” the anonymous witness told the newspaper.
“[The submarine] was completely dark, I could only see it because of the moonlight,” the witness continued according to the report.
Copenhagen Police deputy chief inspector Jens Møller Jensen confirmed to Aftonbladet that he had been in contact with the witness from the freight ship, calling the report an “important piece of information”.
The submarine passed the freight ship at a distance of no more than 30 metres, causing the witness to question the lack of lighting employed by the vessel.
“You just don't do that. Especially somewhere as busy as the Öresund,” the individual said.
The freight ship is reported to have passed the submarine near the island of Saltholm, just over one nautical mile from where it sank the following day. The coordinates have been given to police.
Police have charged Madsen with killing 30-year-old Wall by unknown means.
The Swedish journalist was on board Madsen's UC3 Nautilus submarine before her disappearance on Thursday evening.
Madsen was detained by the court on suspicion of manslaughter, reports TV2 and other media.
Wall was last seen on board the vessel when it left the Refshaleøen island off Copenhagen on Thursday evening.
After his submarine sank at around 11:00am on Friday, Madsen alone was brought to shore on board a private boat.
The submarine owner then reported that his passenger had left the vessel at the Refshaleøen island near Copenhagen on Thursday evening.
But Jensen said at a press conference Sunday that Madsen had since changed his story.
“The accused has given us different accounts,” Møller said according to TV2's report.
“We decided during our first press conference relating to this case to say that he told us he dropped her off at 10:30pm [on Thursday, ed.] at Refshaleøen, and in relation to my saying we have been given different accounts, it is correct to say that we have been given another explanation since,” Møller said.
The submarine was raised from the water on Saturday and searched by police technicians on Sunday, but no body was found.
“I have informed Kim Wall's parents that she is not in the submarine,” Møller said.
Submarine disappearance timeline: What we know so far
Thursday 7pm: The submarine, crewed by its owner Peter Madsen and a Swedish journalist, sails from the Refshaleøen island harbour near Copenhagen.
Thursday 8:30pm: Denmark military authorities receive a message from a cruise ship that observed the submarine sail out of Copenhagen Harbour, according to a DR report.
Thursday night: Nautilus is spotted sailing unusually close to a freight ship with its external lights switched off, according to an anonymous report provided by a witness to Swedish daily Aftonbladet.
Friday 2:30am: The partner of the Swedish woman reports that the craft is missing. The Danish Defence Command (Værnsfælles Forsvarskommando) begins searching for the submarine.
Friday 10:30am: The submarine is sighted in Køge Bay. Radio contact is made and the owner says he is setting course to Copenhagen, and that the submarine has technical problems.
Friday 11:00am: The owner is recovered by a private boat, but there is no sign of the second crew member. The owner is sailed to land at Dragør Harbour.
Friday afternoon: Police in Sweden state that a missing person alert issued during the morning pertains to the woman on board the submarine and remains in place, reports Swedish news agency TT.
Friday 5:44pm: Copenhagen police announce through a press statement that the owner of the Nautilus has been charged over the woman's death. Police divers have located the sunken submarine but have not yet gained access to it.
Saturday afternoon: Madsen is remanded in custody for 24 days by Copenhagen City Court as work to raise the submarine begins and the identity of the woman emerges as journalist Kim Wall, after her family contacts Danish media.
Sunday: The raised submarine is brought to land and police technicians begin their examination, but no body is on board.
Monday 9:30am: Madsen's lawyer informs media that her client accepts his preliminary detainment on charges of manslaughter.