The tabloid said Jamaican police would announce at a press conference next week that they were no longer treating the death as murder and instead now believed he died of heart failure brought on by chronic ill health and possibly diabetes.
The 58-year-old was found dead in his Kingston hotel room. An autopsy indicated that the former England Test player had been strangled.
The day before his body was found, cricketing powers Pakistan had crashed out of the World Cup in the Caribbean in a shock defeat to minnows Ireland.
A myriad of different possible explanations for Woolmer's death have appeared in the world's media.
Following the Metropolitan Police review, Jamaican officers now privately agree that no third party was involved in Woolmer's death, the Daily Mail said in a front-page story.
"Mr Woolmer was not a well man. It is now accepted that he died of natural causes," a source close to the inquiry told the tabloid.
Pervez Mir, Pakistan's media manager during the World Cup, suggested the Pakistan Cricket Board might consider legal action.
"I've been saying all along that Bob had died a natural death and let's not jump the gun, let's wait," he told the BBC.
"The Pakistan team players will be absolutely angry, because of the amount of allegations that were levelled against them, or insinuations, or speculations against the Pakistan team."