As previously reported, a campaign to save Starr's birthplace failed after the city council said it had: "no historical significance". However, National Museums Liverpool said the home would be a "hugely popular" feature.
"Negotiations are underway with all parties involved, but there are still many details to be worked out.
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The house - in Madryn Street in Toxteth - is one of 460 buildings in the area set to be demolished so new homes can be built in their place. Starr lived there for three months before he moved to Admiral Grove.
Work on the Museum Of Liverpool is set to be completed in 2008, reports BBC NEWS.
The same year the city will be the European Capital Of Culture.
