The Supreme Court in Islamabad can approve or reject a call for an appeal against its decision in October 2018 which overturned the Christian women's blasphemy conviction.
In a deal struck with Islamists - who staged days of violent demonstrates immediately after Ms Bibi was cleared - authorities agreed there would be a final review of the controversial ruling.
Ghulam Mustafa Chaudhry, a lawyer who filed the petition demanding an appeal, told the AFP news agency: "The court will determine if our appeal against her acquittal is admitted".
Hardliners, who accuse Ms Bibi of insulting the Islamic prophet Muhammad, have been demanding her public execution.
The mother-of-five has always denied the allegation of blasphemy which followed a disagreement she had with a group of Muslim women in 2009 over the shared use of a water cup.
Ms Bibi spent eight years on death row after being convicted of blasphemy in 2010.
Since her acquittal, she has been living in hiding and under the close watch of security forces.
Supporters and family members are keen for Ms Bibi to leave Pakistan as soon as possible. Countries including Australia and Canada have signalled their willingness to offer her asylum.
If the request for an appeal is declined, Asia Bibi could finally have the go-ahead to exit the country.
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