According to the source, the news conference will be addressed by police commissioner Lucius Thomas, who will read a statement, outline toxicology results and give details of post mortem examinations carried out on Woolmer's body.
The former England international cricketer was found unconscious in his Kingston hotel room on March 18, a day after Pakistan had suffered a shock loss to
The 58-year-old was pronounced dead at hospital shortly after.
Local police decided to instigate a murder investigation into the Briton's death following a release of the autopsy report that stated he had been strangled.
However, a pathologist attached to Britain's Scotland Yard reported that Woolmer died of natural causes, a claim made before by two Pakistan police officers, who were in Kingston as part of the investigating team.
News reports have speculated that Jamaican police would be changing their position from murder to death by natural causes, and police sources believe that Thomas will outline that view at next week's news conference.