Bristol's mayor is urging people to find a spare room in their homes for refugees, as the council says it hopes to take some of the "desperate".
George Ferguson said he would arrange to take somebody in himself and hoped those with "space in their homes" and "generous hearts" would follow.
Bob Geldof is among other people who have offered to take in refugees.
The prime minister has said the UK will accept thousands more Syrian refugees in response to the humanitarian crisis.
Campaigner Geldof said he would take in four families at his homes in Kent and London, telling Ireland's RTE Radio: "It's a failure of that new politics that's led to this... absolute sickening disgrace."
Elsewhere, the Mayor of Liverpool, Joe Anderson, has offered to take 100 refugees into the city.
And the Dean of York Minster, the Very Reverend Vivienne Faull, said the cathedral would offer one of its vacant properties to a family.
'Lead by example'
It has not been decided how many refugees Bristol could take. The city has 13,000 households on the waiting list for social housing.
Mr Ferguson said: "I have a small room that I could offer and I shall do so... I will make arrangements to be able to take somebody in."
The mayor, whose family took in a Ugandan family fleeing Idi Amin's regime in the 1970s, said he wanted to "lead by example".
He said he was not asking people living in crowded housing to take more people. But was looking for those "who do have space in their homes and a huge generous heart" to take people in and help them get back on their feet.
Councillor Brenda Massey said she had been contacted by Syrians in Bristol who were offering help, as well as some of the city's mosques. But she said it was important Bristol had a long-term solution for refugees - with housing, education and health facilities in place.
Calls for Britain to offer refuge to more of the thousands of people fleeing Syria and other countries intensified after a photo was published of a drowned three-year-old Syrian boy.
Labour leadership contender Yvette Cooper said on Tuesday every city should be asked to accept 10 refugee families.
The Local Government Association, which represents councils in England and Wales, said any help offered by councils must be voluntary and Whitehall must cover the costs.
A spokesman for Cosla, which represents most Scottish councils, said a number of them were "in discussions with the Home Office about accepting more" Syrian refugees - if they get support from Holyrood and Westminster.
Source: BBC News
Seeking asylum in the UK
25,771
people applied for asylum in the UK in the year ending June 2015
41%
(11,600) were granted asylum
- 14% of applicants were from Eritrea
- 9% were from Pakistan
- 8.5% were from Syria
- 2,168 applications were from unaccompanied children
Hakuna maoni:
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