Minister for the Environment Dick Roche is in favour of preserving 16 Moore Street, the last headquarters of the leaders of the Easter Rising in 1916.
A spokeswoman for the Minister said Mr Roche would like to see the Moore Street project "progressed" and it was "something very close to his heart".
Conservationist Damian Cassidy
However, she pointed out that the decision was a matter for Dublin City Council and not Mr Roche. The Minister is planning to meet with his department officials today to discuss taking the matter forward.
The council is calling in an architect and urban historian with a view to protecting the property. Last week a campaign was begun by a group wanting to save the building, which has fallen into disrepair.
Representatives of the group talked about the property with deputy city manager Eoin Keegan on Friday in a meeting they described as "very helpful".
"The council has engaged a firm of architects and designers to do a survey of the property and to make recommendations to the council about the possible foundation of a museum there," according to conservationist Damian Cassidy.
"The building is of enormous historic significance as it was the last refuge of the 1916 leaders and is where the surrender document was drawn up. It is in a terrible state and in danger of further decline and vandalism," said Mr Cassidy.
Dublin City Council said architect Grainne Shaffrey of Shaffrey Associates and urban historian John Montague had been commissioned to conduct a survey of the building. However, there is an issue over access to the property and its ownership is in dispute.
The campaign to save it has the support of An Taisce, as well as several politicians, relatives of those who fought in the Rising and conservationists.