Arts organisation Collective Gallery has received initial support in its bid to the Heritage Lottery Fund, which means it will now have two years to work on a detailed bid for a cash award.
The project aims to restore the Grade A-listed City Observatory complex on Calton Hill to the original William Henry Playfair design, create a new gallery space and open up the site to the public for the first time.
The observatory, which is on Scotland's buildings at risk register, was completed in 1822 and opened as The Royal Observatory of King George IV. In 1896 the Royal Observatory that once stood on Calton Hill was relocated to Blackford Hill, and after an overhaul of the interior, the building was renamed the City Observatory.
Richard Lewis, Edinburgh Council's Culture and Sport convenor, said: "This new, world-class complex will combine innovative art and iconic heritage."