The Christian mother of five was placed on death row in Pakistan in 2010 after being accused of blasphemy during a row with colleagues.
She was acquitted last year, after criticism from the international community, but is yet to be freed.
Giving an update in Parliament on Tuesday, Foreign Secretary Jeremy Hunt said: "Making sure that she is safe and has somewhere safe to go is a top priority for this government.
"We have had numerous discussions in private with a Pakistani government about how to progress this.
"We are making progress and I'm very hopeful that this will have a positive outcome."
It's unknown why Asia Bibi remains in Pakistan. Her family have fled to Canada.
The UK government has previously refused to address whether it would offer her and her family asylum but has insisted it is working behind the scenes to find a resolution.
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