The family has appealed for answers as to what happened to her, reports Danish media TV2.
Wall's parents and brother told the broadcaster via a written message that her family is now facing the loss of their daughter and sister, but appealed to authorities to help them find closure.
“Kim has worked in many dangerous places as a journalist, and we have often been worried about her,” the family wrote to TV2.
“That something like this could happen in Copenhagen, just a few kilometres from her childhood home, we could never have imagined. It now seems as though the worst thing has happened,” the message to TV2 continues.
“We – Ingrid, Joachim and Tom Wall – therefore appeal to anyone who, in any way, can help us to find out what happened.”
The family wrote that they hope clues that can provide answers to the case can still be found.
“There is nothing we would like more than to than for Kim to turn up alive, but we have to admit that the chance of that happening is extremely small.
“Let us find certainty about what happened.”
READ ALSO: Kim Wall presumed dead: Copenhagen Police
Freelance journalist Wall vanished after having boarded the 18-metre UC3 Nautilus sub on Thursday evening last week, apparently as part of her work on a feature story about its owner, inventor and entrepreneur Peter Madsen.
Madsen alone was brought back to a harbour on Copenhagen on Friday after the vessel sank in waters near Køge Bay.
The Swede's body was not found inside the submarine after it was raised and brought to Copenhagen for forensic examination.
Earlier this week, police stated that they would not release details of the evidence found on board the vessel, in order to avoid prejudicing the ongoing investigation.
46-year-old Madsen is accused of negligent manslaughter and was on Saturday remanded in custody for 24 days.
Swedish and Danish authorities are now cooperating on the search for the missing reporter.