Repeated attempts by Nguyen's lawyers and Australian authorities to convince Singapore to drop the death sentence have failed, and a request by his mother to hug her son was refused.
But Singapore's foreign ministry, in a statement released by its high commission in Canberra, said a contact visit between Nguyen, his mother Kim and twin brother Khoa would be permitted.
The statement said the decision was made in response to a personal request by Australian Prime Minister John Howard to his Singaporean counterpart Lee Hsien Loong, at a Commonwealth heads of government meeting last week.
But a hug will not be allowed, with Singapore arguing that "such encounters can be traumatic and are likely to destabilise the prisoners and their family members."
Nguyen's lawyer Lex Lasry earlier said it would be inhumane for Singapore to deny a last embrace, and Australian Foreign Minister Alexander Downer has continued pleading with Singapore to permit a contact visit.
Nguyen, 25, has only been allowed to see family and friends through a glass partition at Singapore's Changi prison since being sentenced to death for trying to smuggle 400 grams of heroin via Singapore to Australia in 2002.
He is set to be hanged at 6am Singapore time (9am AEDT) at Changi prison.
Kim Nguyen, who has not spoken to the media since she arrived in Singapore on November 21, has appeared increasingly strained as she visits the prison.
Mr Lasry said she is coming to terms with the impending death of her son.
"She is very distressed but in some ways she has realised that this is something that she has to come to terms with and I think courage in that family is shared amongst mother and son."
He said his final visit to his client was unforgettable.
"It was extremely difficult, of course. Emotional, But you have to say it was a satisfying hour and a half, unforgettable," said the lawyer, who struggled to maintain his own composure.
"The thing that strikes me about this is we were looking into the eyes of a healthy young 25-year-old man with so much to offer who is going to die a violent death. The violence of the death he is going to die is so much at odds with the sort of person he is.
"I just find it an appalling injustice," said Mr Lasry.
Fellow lawyer Julian McMahon said Nguyen is in a "beautiful state of mind", describing him as completely rehabilitated, reformed and focused on doing what is good, "and now they are going to kill him."
Extradition attempt
Even on the last day of Nguyen's life, efforts are being made to save him.
Melbourne lawyer Brian Walters issued private action against him, in the hope that Australia could seek his extradition.
Mr Walters charged Nguyen with two counts of conspiring to import heroin and one count of conspiring to traffic heroin, with a summons requiring Nguyen to appear at Melbourne Magistrates Court on February 2 next year.
Hangman visit
Preparations for Nguyen's execution are underway, with the condemned man receiving a visit from Singapore hangman Darshan Singh, who weighed Nguyen to establish the correct length of rope needed.
After saying his final farewells, Nguyen was served a final meal, and is meeting with chaplain Father Gregoire Van Giang.
He is due to be hanged at 6am local time (9am AEDT).
At that very moment, at Melbourne's St Ignatius Catholic Church, where Nguyen and his brother once went to school, the bell will ring out 25 times, once for every year of the dead man's life.
Within hours of the hanging, Nguyen's body will be returned to his family, and flown back to Melbourne for his funeral.