Woolmer, 58, was found dead in his Kingston hotel room on March 18, the day after cricketing powers Pakistan crashed out of the World Cup in an upset loss to minnows Ireland.
But the Jamaican police said Sunday they are standing behind their belief that Woolmer was murdered.
"That will remain our position until such time as the results of the investigation are known; including the forensic and pathology analysis," said Jamaica Constabulary Force (JCF) director of communications Karl Angell in a news release.
Woolmer's death led to a fevered round of speculation. One theory was that his death was linked to match-fixing and illegal betting in cricket, and investigators from Britain and Pakistan were drafted in to help with the probe.
But the Jamaican Gleaner said that a pathology report submitted by Scotland Yard detectives stated that Woolmer "died of natural causes and not manual strangulation as was initially reported by Deputy Commissioner Mark Shields."
"The Scotland Yard report specifically said Woolmer died of heart failure, contradicting earlier reports by the investigative arm of the Jamaica Constabulary Force and local pathologist, Dr Ere Sheshiah, who had conducted a post-mortem on Woolmers's body," the paper said.
The Scotland Yard findings "were disclosed last week during a meeting with Jamaica's Deputy Commissioner of Police Mark Shields and Superintendent Colin Pinnace, who stopped over in London en route to South Africa" where they were heading to meet with Woolmer's family, it added.
Said Angell, "The speculation made in Sunday's newspapers is part of a series of unhelpful reports that have appeared in the media throughout the duration of this investigation," Angell continued in the release.
"The JCF is conducting an extensive and thoroughly professional investigation into the circumstances surrounding the death of Bob Woolmer.
"This has included a request to the Commissioner of Police of the Metropolitan Police Service (MPS) in London to conduct a review of the investigation," the release further quoted Angell saying.
It was also reported on Saturday, that the Jamaican police were close to naming Woolmer's killer.
"The JCF would again urge the media to refrain from speculation because of the additional distress it places upon the Woolmer family and the fact that it can hinder the progress of the investigation," the release added.
Angell also disclosed that Shields and Deputy Superintendent Colin Pinnock have met with the Metropolitan Police review team and the pathology and forensic experts in London.
Angell also said police have departed for South Africa to brief Gill Woolmer and her family on the progress of the investigation.
In addition to their working relationship with Scotland Yard, Angell, said, "due to the open and transparent approach to the Woolmer investigation, the JCF has also welcomed assistance of the Pakistani authorities and INTERPOL."