Lynda Spence, 27, of Glasgow, has debts of more than £100,000 and has had business dealings with people who are known to police.
The news came as her mother broke down while she made a plea for her daughter to come home.
Patricia Spence, 55, joined police to call for information about her daughter, who went missing in April.
It is feared she may have fled to escape from people she owed money to or that she may have come to harm from people seeking to be reimbursed.
Detective Superintendent Alan Buchanan, of the major investigation team at Strathclyde Police, said officers were checking her financial history in an attempt to shed light on her disappearance.
Ms Spence, also known as Lynda Zefaj, Lynda Palmer, or Lynda Reilly, was involved in the financial sector, securing mortgages, and a business called Fraser Developments, based in Great Western Road, in Glasgow’s West End.
Detective Superintendent Buchanan, who is leading the investigation, said: “This is totally out of character for Lynda. Her parents are distraught.
“She owes money to a number of people. Some of these dealings are legitimate and some are with people known to police -- people who could be a danger if she was in debt to them.
“We don’t know if Lynda has decided to disappear because of these dealings or she has come to some harm at the hands of people she owes money to.”
Ms Spence, from Castlebank Street, Partick, was last seen by her parents on April 13 when she visited them at their home, also in Partick.
She then stayed with a friend overnight in Maryhill, but left around midday on April 14.
She indicated she was going to London, but there is no evidence she arrived there.
Mr Buchanan added: “Her business went into severe financial difficulties and owes a number of people money. We are trawling through all the people she was involved with financially, although some are being more co-operative than others.
“I am appealing to Lynda to contact us or walk into any police station.”
Ms Spence’s distraught mother Patricia, with her husband James, 67, by her side, also urged her daughter to contact them.
Her mother said: “Lynda, if you are listening please come forward and let us know you are safe or let someone know.
“We are worried about you and whatever has happened it doesn’t matter. It is Father’s Day on Sunday -- please contact us and let us know you are okay.”
The day after she disappeared, a text message was sent from Ms Spence’s phone to her mother. It said she was in London.
A week later, on April 20, her silver Astra was pictured on the A77 at Floak. The car’s nearside wing mirror was damaged.
Then, on June 2, an old Nokia phone belonging to Ms Spence was found in a wheelie bin outside a sandwich shop in Holmhead, Kilbirnie, Ayrshire. It had not been used for months, and police confirm it was not the phone used to send the text message on April 14.
Ms Spence is 5ft 8in, and wears her brown hair in a ponytail.
She is tanned, has a scar under her eye and is known to frequent Glasgow’s West End and parts of Ayrshire.
Anyone with information should call police on 0141 532 3270 or Crimestoppers anonymously on 0800 555 111. Police can also be contacted by text on 07864 178454 or through the dedicated email address lyndaspenceenquiry@ strathclyde.pnn.police.uk