It comes after former Foreign Secretary Boris Johnson, and other politicians, urged the government to help her.
Ms Bibi was freed last week after eight years on death row, sparking violent protests in Pakistan from Islamists.
Her husband has said the family is in danger and has pleaded for asylum from the UK, US or Canada.
Prominent British Muslims, including three imams – Qari Asim, Mamadou Bocoum and Dr Usama Hasan – have written a letter to Home Secretary Sajid Javid asking him “to make a clear and proactive statement that Britain would welcome a request for sanctuary here”.
The letter, also signed by MPs from across the political divide, goes on: “We are confident that action to ensure Asia Bibi and her family are safe would be very widely welcomed by most people in Britain, across every faith in our society.
“If there are intolerant fringe voices who would object, they must be robustly challenged, not indulged.”
The head of government agency the Commission for Countering Extremism also said granting Ms Bibi asylum was “right thing to do”.
Sara Khan said: “This is an opportunity to send a clear message to extremists that our country will stand up for our values.”
Who is Asia Bibi ?
The mother-of-five was the first female non-Muslim charged under Pakistan’s blasphemy laws.
The laws carry a potential death sentence for anyone who insults Islam.
Asia Bibi, sometimes known as Asia Noreen, was convicted in 2010 of insulting the Prophet Muhammad during a row with neighbours the previous year. Her lawyers have denied she ever did so.
The court overturned her conviction on the grounds there was not enough evidence to support it.
Where is she now?
Pakistan has reached a deal with Islamists to try to stop her leaving the country to help calm the unrest which has broken out following her release.
But to take the official route to asylum, the family would have to flee Pakistan and then make their request.
Canada has said talks are under way about allowing her to go there.
By Dominic Casciani, BBC home affairs correspondent
This public call from progressive Muslim community activists and thinkers, urging Mr Javid to come to Asia Bibi’s aid, is a clear indication, if ever there needed to be one, that there is no such thing as a single “community” with a single point of view.
Among the signatories are some of the most radical religious thinkers in the UK who have been, slowly, but surely, chipping away at conservative interpretations of Islam.
Some of the signatories have spent time in prisons challenging convicted terrorists to drop their hostility to the UK.
They and others – often quietly – seek to demolish the extremist world view that human rights – such as freedom of speech and choice in religion – are somehow incompatible with Islam.
The fear that many of these thinkers have is that if the UK does not offer to protect Asia Bibi, then extremists will be emboldened to further spread their message.
Which politicians support her?
Boris Johnson was reported in the Daily Mail as saying “we cannot allow the threat of violence to deter us from doing the right thing.”
In a letter to the home secretary, he went on: “I do not think it is a dignified position for the UK, given our historic links with Pakistan and the extent of our influence there, to look to others to do what we are allegedly nervous to do ourselves.”
Conservative MP Rehman Chishti, who has spoken to Ms Bibi’s husband and daughter, says her life is in “grave danger”.
He told BBC Radio 4’s Today programme: “We have a moral obligation as the United Kingdom to give sanctuary to someone who’s been persecuted for their faith.”
Diane Dodds, DUP MEP for Northern Ireland, wrote on Twitter that the UK should “grant asylum immediately”, calling on the home secretary to “do the right thing”.