Canberra said it is willing to grant asylum in the event that talks to bring Asia Bibi and her family to Canada stall.
The development was welcomed by campaign group The Australian Christian Lobby, which urged ministers to "act now".
Managing director, Martyn Iles said: "This is momentous news for all who have lobbied so hard and so long for Asia Bibi."
It remains unclear what progress has been made since Prime Minister Justin Trudeau revealed two weeks ago that Canada was "in discussions" with Islamabad about Ms Bibi.
Mr Iles continued: "Government sources have this afternoon confirmed that it will make an offer of asylum to Asia Bibi if Canada does not do so in the coming days.
"This announcement means that both her and her family have been guaranteed a home in one of the freest and safest countries on earth."
Earlier this month, Italy's deputy Prime Minister Matteo Salvini said he would do "everything humanly possible" to secure her safety.
Nationwide protests by hard-line Islamists erupted in major Pakistani cities when Ms Bibi was acquitted at the country's Supreme Court.
She had been on death row since 2010, when she was convicted of insulting the Islamic prophet Muhammad.
Since her release from jail, Ms Bibi has been kept at a secret location in Pakistan. Her family is also in hiding.
Hardliners want to stop her leaving the country while judges consider calls to review their decision.
Mr Iles added: "It's hard to see any justification for waiting on Canada.
"Either it's the right thing to do or it isn't. And with extremists hunting her from house to house, it is important for us to act now.
"It seems she has three possible destinies ahead of her: Australian, Canadian, or dead. It would be the ultimate tragedy if she were to die on account of bureaucratic dithering."
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.