Andrew Chan and Myuran Sukumaran, ringleaders of the so-called "Bali Nine" drug smuggling gang, were arrested in 2005 and sentenced to death the following year after being caught trying to traffick heroin out of Indonesia.
The pair recently lost their final appeals to Indonesian President Joko Widodo for clemency despite arguing that they had rehabilitated themselves in prison.
Indonesian authorities are pushing ahead with the planned executions, which are expected to be carried out this month.
Authorities have repeatedly said the appeal for presidential clemency is a death row convict's final chance to avoid the firing squad, but the men's lawyers believe the latest move could at least delay the executions.
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Lawyer Doly James said he hoped that if a judge granted a preliminary hearing, the executions would be postponed.
"There is no guarantee," he told AFP, but added: "The attorney general's office should respect the ongoing legal process."
Widodo has been a vocal supporter of capital punishment and warned Indonesia is in a state of emergency due to drugs, with dozens of people dying every day.
The men's lawyers claim it is "unacceptable" for the president to use blanket arguments to refuse the men clemency.
Chan and Sukumaran's mothers travelled to Jakarta this week to plead for their son's lives, claiming they had changed during a decade behind bars and deserved a second chance.