The inquiry into the deaths of four young soldiers at the Deepcut barracks in Surrey is understood to have found no evidence that any of the recruits were murdered.
Geoff Gray died at Deepcut in 2001, James Collinson the following year
The investigation by Surrey Police was launched last year after serious doubts emerged about earlier judgements that all four cadets had committed suicide.
The report is expected to be sent to the Coroner's Office next week.
The four privates who died were Cheryl James, from Llangollen in north Wales; Sean Benton, from Hastings in East Sussex; Geoff Gray, from Seaham in County Durham; and James Collinson, from Perth in Scotland.
The parents of 17-year-old Private Collinson have always denied the army's claims that their son killed himself.
The dead soldiers
Sean Benton, 20, from Hastings, East Sussex, 1995
Cheryl James, 18, from Llangollen, north Wales, 1995
Geoff Gray, 17, from Seaham, County Durham, 2001
James Collinson, 17, from Perth, Scotland, 2002
Their local MP, the Scottish National Party's Annabelle Ewing, said she had serious misgivings about the police report.
"If this speculation is correct and Surrey Police have concluded already that there was no third party involvement in the deaths of James Collinson and the other soldiers, then I think certain key questions arise.
"Firstly, how can they yet have reached a conclusion when I understand they are still awaiting the report of the independent ballistics expert Frank Swann?
"And when they make public their findings next week I wonder what weight can be placed on their conclusions in light of the fact that, in my view, their investigation was fundamentally flawed because no proper forensic evidence gathering was carried out at the outset."
Ms Ewing said she believed that if the police inquiry does rule out foul play there will still be unanswered questions.
The MP insists that a full judicial inquiry is the only way to discover what events took place at Deepcut and how the matter has been handled by the Ministry of Defence.
The independent forensic expert Frank Swann was hired by the families to investigate the deaths.
Geoff Gray, whose 17-year-old son Geoff died at Deepcut, reacted angrily to reports that police had already
revealed the likely conclusions of their inquiry.
"I am absolutely raging," said Mr Gray.
"I am so annoyed. It is just appalling, this is the final slap in the face.
Cheryl James and Sean Benton both died at Deepcut in 1995
"They have strung us along and along for so long.
It just goes to show how incompetent Surrey Police are."
Mr Gray said he had been supposed to be meeting a senior detective from Surrey Police later this week to discuss the findings of the report.
"We haven't seen the report, we were meant to sit down on Thursday and work out how it was going to be presented," he said.
"I can't see the point of it now. What chance have we got to get an investigation into my son's death?"
Surrey Police confirmed that the results of its investigation would be unveiled next week.
But a spokesman for the force refused to give any indication about the contents of the report.
A team of 30 detectives from Surrey Police has interviewed more than 400 witnesses during the course of the year long investigation.
The inquiry was launched in the wake of the death of Private Collinson in March 2002, partly in response to the concerns expressed by the families of the recruits about their deaths.