The Christian mother-of-five was acquitted last October after spending eight years on death row for blasphemy.
However, hard-line Islamists want her publicly executed.
Countries including Australia and Canada have signalled their willingness to offer her asylum.
Diplomatic sources have told the Telegraph that Canada is a leading contender to offer asylum to Ms Bibi if Pakistan's most senior court dismisses a challenge against her acquittal.
After days of protests by hard-line Islamist clerics, Imran Khan agreed to allow a petition against the decision.
Ms Bibi has been forced to live under close protection in a mystery location since her 2010 conviction and death sentence was quashed.
Supporters and family members are keen for Ms Bibi to leave Pakistan as soon as possible.
Her husband and family have decided they will be unable to live safely in Pakistan if she is freed, with prominent figures and even some of her neighbours still calling for her to be killed.
Meanwhile, new research published by the Catholic Church has found there are 187 live cases of Christians in Pakistan facing blasphemy charges.
Suspects face execution or life imprisonment if found guilty.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
