Woolmer says he "would like to sleep on my future as a coach" after Pakistan's shock defeat to debutants Ireland and exit from the World Cup.
After being found unconscious in his hotel room, he is later declared dead in hospital.
Woolmer's son, Russell, tells a South African radio station that doctors told him the cause of death may have been either stress or a heart attack.
The coach's family authorises local authorities in Kingston, Jamaica, to carry out a post mortem.
Pakistan Cricket Board says findings from a post mortem were "inconclusive" and further tests were being carried out
Jamaican police say they are treating the death as "suspicious" and will continue a full investigation.
Woolmer's wife, Gill, says she does not suspect foul play in an interview with an Indian news channel.
Pakistan play their final match at the World Cup against Zimbabwe and dedicate their win to Woolmer.
Jamaican police launch a murder investigation into his death, saying "the pathologist's report states that Mr Woolmer's death was due to asphyxia as a result of manual strangulation".