Imran Khan, the former international cricketer, claimed a "complication" has delayed the departure of Asia Bibi - who remains in a secure compound at a secret location.
He told the BBC: "There is a little bit of a complication. And I can't speak on the media about [it].
"But I can assure you she is safe and she will be leaving in weeks".
Hardline Islamists - angry at Ms Bibi's acquittal by the Supreme Court in Islamabad last October - have been demanding that the 53 year old be publicly executed.
She spent nine years on death row after being convicted of insulting the Islamic prophet Muhammad. Ms Bibi has always denied any wrong-doing.
The mother-of-five was accused of blasphemy after a row involving a group of Muslim women over the use of a water cup.
The case has drawn fresh attention to Pakistan's controversial blasphemy laws, which human rights campaigners fear are regularly misused to persecute Christians and settle personal scores.
Several Western countries have offered sanctuary to Asia Bibi. There has been speculation she intends to joins her daughters who fled to Canada.
Asia Bibi's husband, Ashiq (middle), and one of her daughters, Eisham (right). Pictured with Premier's Alex Williams in 2018.
Despite the insistence of Pakistani officials that she is a free woman, Ms Bibi has been confined to a safe house - apparently for her own safety.
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.