Liverpool Council boss Joe Anderson is promising the city will "do the right thing" on the future of the historic Welsh Streets.
His pledge comes as an olive branch to Beatles fans, remaining residents and heritage campaigners who have united in opposition to demolition plans.
The estate of Victorian terraced homes in the Dingle area of the city includes the birthplace of Beatles legend, Ringo Starr.
And Number 9 Madryn Street, Ringo's home to the age of four, has been the subject of a high-profile campaign by Beatles fans in the UK and overseas, to save it for posterity.
A group of residents from the Dingle and the Liverpool Civic Society have also voiced opposition to demolition.
They say "retro-eco-fit" refurbishment is feasible at an economic cost and point to the fact that there is no longer government funding in place for building new homes on the site.
Tory Housing Minister Grant Shapps has also pressed the council to reconsider the future of the Welsh Streets - a move that Labour councillor Mr Anderson had appeared to dismiss.
But Cllr Anderson, who is in charge of the city's housing policy, has now confirmed that the town hall will consider renovation as an option.
Cllr Anderson said: "Nobody wants to demolish for the sake of demolishing. We want to do what is right for the sake of the local residents and the area.
"I want the best resolution to the problem.
"Doing nothing is simply not an option. I am not prepared to undertake an operation that is not financially viable."
Cllr Anderson's comments come as the specialist property company, Regeneration Express, revealed that it has held talks with officials over plans that could save the Welsh Streets.
Philip Coppell, a Beatles tourism guide and Chairman of the Save Madryn Street campaign said: "It's very encouraging to hear that Mr Anderson saying that the city wants to do the right thing.
"There are millions of Beatles fans all over the world who believe the right thing is to preserve 9 Madryn Street because of its historic significance as Ringo's birthplace.
"There are also many people in Liverpool, including residents in the the Welsh Streets and the surrounding area, who want to see the entire estate of homes saved from demolition rather see the area simply grassed-over.
"I have asked Cllr Anderson for a meeting to discuss the alternative options and I hope he will now agree to hear what we have to say.
"There is a viable offer on the table that could see the homes renovated. As part of that plan we want to see the importance of Number 9 Madryn Street fully taken into account."
Barbara Smith, Liverpool 8 around 1 year, 1 month ago