The Islington Primary Care Trust (PCT) has said an assessment is being carried out into the refurbishment of the Grade I-listed building.
The move follows growing concern from the architectural community, which has put increasing pressure on the council and the PCT to take action over the building's future.
The PCT statement said: 'The project is in its very early stages and we are currently considering our options. The refurbishment is not straightforward because the building is Grade I-listed.
'The PCT is carefully considering the implications of this status, in terms of what can and cannot be achieved within the constraints of the building, and the extra cost of the conservation element of the project.'
Designed in 1935 by Lubetkin - a pioneer of Modern architecture in Britain - the Finsbury Health Centre was the first achievement of the Finsbury Plan, an effort to create better living conditions for residents of the north London district.
The building underwent the first phase of refurbishment nearly 12 years ago, with the work undertaken by John Allan of Avanti Architects.
Allan, who was a close friend to Lubetkin, said he was pleased to hear of the planned refurbishment work.
'It's welcome news that a refurbishment is going to take place, provided it is a sensitive and well-conceived scheme,' he said.
'I have various ideas of what I think needs to be done to the building, but I am not involved with the work.'
An architect is yet to be named to carry out the work, although Purcell Miller Tritton Architects is producing a conservation management plan, setting out guidelines on what can be done without compromising the building.
Purcell Miller Tritton also produced a conservation statement on the building two years ago.
Jane Kennedy, principal at Purcell Miller Tritton, said: 'It is not our first involvement with the project, but we are still very pleased to be working on it.
'The building needs adaptation for modern use, and some very careful repairs will have to be carried out. We are working very closely with English Heritage and Islington's conservation officer to make sure this is achieved.'
Kennedy said she was well aware of the building's significance, especially in its social context, and that was why a detailed conservation plan was being drawn up.
'It's a very important building,' she said. 'One of the most important 20th-century buildings in England, in fact. And this is not only because of its architecture, but also for its social ideas, about creating better living conditions for the area - it holds a dual importance.'
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