If listed, the Modern building will join Edinburgh Castle and the Scott Monument on the city's prestigious list of historic buildings.
The decision has been backed by a number of Scottish architects including Malcolm Fraser, who said the RMJM store is one of the few Modernist additions to Princes Street that should be saved.
Speaking to the Edinburgh Evening News, Fraser said: ‘It's popular for people to look at the 1960s and think everything was rubbish, but we need to understand there are also some good buildings from that time.
‘If you look along Princes Street, 75 to 90 per cent of the 1960s buildings are dreadful and need to go. But in Scotland we always seem to get rid of the best ones first.’
‘The '60s caused such damage to Princes Street that a reaction that says "Tear it all down" is understandable. But the materials used in the building were better, and it was done with much more finesse and care than the other 1960s additions to the street,’ he added.
A Historic Scotland spokesperson confirmed the building was being considered.
‘We are about to go out to consultation with the owners,’ she said.