Friends of Nguyen, visiting him in Singapore's Changi Prison, said he is in surprisingly good spirits, is at peace and living his last days to the fullest.
This comes as sacked Singapore hangman Darshan Singh hinted that a last minute reprieve may not be out of the question.
"Maybe they may say at the eleventh hour... they may give him a life sentence, it's still possible," said Singh, who has conducted hundreds of executions.
Nguyen's lawyer Lex Lasry left Melbourne for Singapore on Tuesday, and admitted his client's case looks "close to hopeless".
"This is a young man who is ready to die, and he's ready to die a good death and a brave death," he said.
However he said his team is still urging Singapore to reconsider its position on the mandatory death penalty.
Friends and family visit
Nguyen's distraught mother Kim, his twin brother Khoa and friends Kelly Ng and Bronwyn Lew have continued saying their goodbyes in extended visits.
"He looks very well, he's been keeping himself very well, and I think that's just because he wants to live life to the fullest while he still can," said Ms Ng.
"It's quite clear that he has accepted what is going to happen and that his primary concern is how we are going to be coping and whether or not we are going to be okay," said Ms Lew.
The pair said Nguyen, 25, has made plans for his funeral, including selecting songs to be played.
One last hug
Australian Foreign Minister Alexander Downer has appealed to the Singapore government to permit Kim Nguyen to hug her son before he is hanged.
"I would have thought it's not an unreasonable thing for a mother to hug her son before the son is executed," said Mr Downer.
The Australian government has argued that the circumstances of the case -- including Nguyen's assistance to Singapore and Australian police, his remorse and his lack of a prior conviction -- constitute grounds for sparing the Melbourne man from the mandatory death sentence.
However repeated requests have failed to move Singapore.
"We've looked at other issues, the impact of other agreements we might have with Singapore, extradition agreements and so on, but there's really no basis in our view that we can find to take any further legal action," said Mr Downer.
"All we can continue to do -- as a government, as a parliament and as a broader Australian community -- is plead for clemency."