Gately died in his sleep yesterday while on holiday in Majorca with his partner Andrew Cowles.
The Times reports that police investigating the case have found no suicide note and no signs of violence.
A Bulgarian man who had been invited to the couple's apartment is being sought by police. A source said: "We do not think this man is involved in any way in Stephen's death but his testimony could prove vital."
Gately had spent Friday night out drinking with Cowles before returning to the apartment. The police were called at 1.45pm on Saturday, where they reportedly found the popstar in his pyjamas.
"There was no suicide note or evidence of any drug use or excessive drinking and the dead man's friends were at a loss to explain what happened," an insider said.
An investigator added: "He was in a strange position. He was squatting on the sofa, almost in a praying position."
The police will reportedly try to establish whether the singer had any medical history which may have caused his death.
The post-mortem is expected to take place on Tuesday because tomorrow is a bank holiday in Spain. The results and a toxicology report are expected by Wednesday.
> Tributes flood in for Gately