Former attorney general Dominic Grieve has urged the Prime Minister and the Home Secretary to extend to Asia and her family permission to seek refuge in the UK.
Mr Grieve said the treatment of Ms Bibi - who spent eight years on death row after being convicted of blasphemy - had been "deplorable" and he urged ministers to intervene.
Referring to Asia and her family, he told Premier: "It seems to me quite clear that their future in Pakistan is an impossible one, in view of the threats they're under.
"They're, therefore, eminently eligible for asylum and I would hope that the United Kingdom government would be in a position to make that offer."
Thousands of people took to the streets of Pakistan's major cities in protest last week after the country's Supreme Court acquitted Asia Bibi. Demonstrators demanded she be publicly executed.
Asia Bibi had been accused of insulting the Islamic prophet Muhammad during a row with a group of Muslim women in 2009. She had always denied any wrongdoing.
Conservative MP for New Forest West, Sir Desmond Swayne told Premier many Christians in the UK were supportive of Asia Bibi's plight.
He told Premier: "There's no question of the right to asylum in this case and I would think, yes, given the strength of feeling that's been felt by so many of the churches in this country, it would be proper to offer asylum."
The Home Office said it does not comment on individual cases
Click here to listen to Premier's Alex Williams speaking with former attorney general Dominic Grieve:
Click here to listen to Premier's Alex Williams speaking with MP Sir Desmond Swayne:
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.