A month on from the killing, and despite 30 officers, assisted by Scotland Yard, working on the case, Jamaican police say they are no nearer to catching the killer.
"There are three possibilities," said Mark Shields, the Jamaica Deputy Commissioner of Police, here on Saturday.
"One is that someone could give themselves up. Two, there could be a massive breakthrough or, three, we are here for the long haul.
"At the moment we are certainly in category three. We would love to move to one but I think that is unlikely at this stage."
The 58-year-old Woolmer was found unconscious in his hotel room on March 18, a day after his Pakistan team had been humiliated at the World Cup by Ireland's part-timers.
He was pronounced dead at hospital and a subsequent post-mortem conducted by government pathologist Ere Sheshiah found that death was due to asphyxia due to manual strangulation.
Shields said that police have now received the toxicology report on Woolmer's tissue sample, but are tight-lipped as to whether the Pakistan coach was poisoned before being strangled to death.
"We have some results from toxicology now but they will require further investigation and analysis and therefore it would be totally inappropriate for me to elaborate any further on that," said Shields.
Meanwhile, Scotland Yard detectives who are assisting the Jamaican police in the investigation, have made some recommendations to local police but Shields was reluctant to comment on the nature of those suggestions.
Detectives are also continuing to analyse CCTV footage recovered from the hotel and elsewhere.
Shields said the police have received some results from these tapes and he said they are encouraging.
Around 30 police investigators are working full-time on the Woolmer investigation with over 100 witness statements taken. Two Pakistan police are also working on the case.
Shields added that Jamaican police will travel oversees as part of the ongoing investigation. The inquest into the death has been set for April 23.
Patrick Murphy, the Kingston coroner, will conduct the hearing at the Jamaica Conference Centre and a dozen or more witnesses are expected to testify.
Woolmer's death led to a fevered round of speculation as to a motive. The most common theory is that his death was linked to match-fixing and illegal betting in cricket.