Maythem Kamil Radhi is set to face trial in October for allegedly being part of a syndicate that put 421 people on an overcrowded and dilapidated vessel known as SIEV-X in 2001.
The attempt ended with 353 people drowning, 146 of them children, in Indonesian waters.
The 45-year-old is not charged over the deaths. He is facing one count of bringing groups of non-citizens to Australia.
Prosecutors argue Radhi played a "facilitation" role before the ill-fated voyage left Indonesia, crown prosecutor Daniel Caruana said during an earlier committal hearing.
Barrister Mark McCarthy applied in the Brisbane Supreme Court on Tuesday for Radhi to be bailed to return to his wife and children in New Zealand.
Alternatively he could live with a family friend in Sydney.
An arrest warrant for Radhi was issued in a Brisbane court in 2011.
But the process was delayed while his eligibility for extradition was argued in courts in NZ, where he had been living with his wife and three children since being accepted as a refugee in 2009.
Radhi surrendered in October 2019 after deciding to stop pursuing appeals against his extradition.
Mr McCarthy said Radhi did not flee while challenging his extradition for eight years, and could face as little as three more months in custody, if found guilty.
"There is a powerful disincentive for him to flee and a powerful incentive for him to attend his trial and to complete this matter," he added.
Mr Caruana opposed the application saying the risk of Radhi failing to appear in court if released on bail is unacceptable, especially with the matter "being so close to finalisation".
Justice Paul Freeburn refused the application.
"On balance it seems to me the proximity of the trial sways the case against granting bail," he said.
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