The Canongate building, just off Edinburgh's Royal Mile, was Smith's home between 1778 and 1790.

It has been used in recent years as a centre for troubled youngsters by Edinburgh City Council, which has put it on the market for £700,000; however, analysts expect the property to attract bids approaching £1 million.

The building has been A-listed - the maximum level of protection for a property - but includes planning permission to convert for residential or commercial purposes.

Kate Morgan, sales agent for Rettie & Co’s land and development department, told The Scotsman: “It is close to the Scottish Parliament and the planned new Caltongate development. Developers know that the area is up-and-coming so it is possible that a local developer will buy and maybe sit on.”

The Canongate building was originally erected for the Earl of Panmure in 1691.

Campaigners oppose the decision by the council and fear the historical value of the building could be lost in the hands of a developer.

Economists from the University of Edinburgh have launched a campaign opposing the sale, expressing the view that the public would be better served by using the building as a policy institute for economics in Scotland, or a study centre for the Scottish Enlightenment.

However, as pointed out by Tatiana Kornienko, a member of the campaign and an economist at the University of Edinburgh, with the closing date for bids on 4 April, it would be impossible to raise the funds to buy the house themselves.

“We can understand that the Council needs money to run its social services, schools, help for vulnerable people,” Kornienko said.

“Our only frustration is that the Council put the house on the market without any advance warning." The campaign team from Edinburgh University is now trying to bring together possible investors.

However, the director of the Adam Smith Institute, Dr Eamon Butler, has questioned the value of an Adam Smith museum.

“Even if we thought we could manage to buy it, what can we do with it? Whether there are enough artefacts to make a museum that takes up a whole house is not known. But it would be nice if whoever buys it remembers him in some way and gives people something to look at,” he told The Scotsman.