The cabinet minister accused of historical rape is set to identify himself on Wednesday, after NSW police on Tuesday declared their examination of the claim “closed”.

The push by the friends of the alleged victim – who took her own life in 2020 – for an inquiry into her allegation has rocked the government since they sent a letter to Scott Morrison and several other parliamentarians last week.

The minister has strongly rejected the allegation in his talks with Morrison, and will do so publicly when he identifies himself.

The naming will be a relief to many male cabinet colleagues, who have had a collective cloud hanging over them amid speculation about his identity.

Morrison, who has rejected the calls for him to set up an inquiry, on Monday said the matter must rest with the police. But the federal police referred it to the NSW police, to whom the woman spoke – without making a formal statement – a year ago.

Government sources on Tuesday pointed as a precedent to what then opposition leader Bill Shorten did. Shorten in 2014 went public after a police investigation into an historical rape allegation concluded without any action being taken. The Victorian police said at the time they had “sought advice from the Office of Public Prosecutions, which advised there was no reasonable prospect of conviction”.

The difference between the two situations is the Victorian police were able to investigate fully because they were dealing with a living alleged victim.

The NSW police said on Tuesday that in November 2019, a 48-year-old woman had attended an Adelaide police station “seeking advice about reporting historical sexual offences, which allegedly occurred in 1988 in Sydney.

“The matter was then referred to the NSW Police Force and an investigation by the Child Abuse and Sex Crimes Squad commenced under Strike Force Wyndarra.

“NSW Police Force has been the lead agency in respect to this investigation since February 2020.

“For various reasons, the woman did not detail her allegations in a formal statement to NSW Police. The woman passed away in June 2020.

“Following the woman’s death, NSW Police came into possession of a personal document purportedly made by the woman previously.

“NSW Police have since sought legal advice in relation to these matters. Based on information provided to NSW Police, there is insufficient admissible evidence to proceed.

“As such, NSW Police Force has determined the matter is now closed.”

The minister has hired well known defamation lawyer Peter Bartlett.

Former deputy prime minister Barnaby Joyce said Morrison should get a retired judge to examine the matter and report to the Prime Minister’s department.