More than 200 bids have been made for the Tardis-style boxes, after Lothian and Borders Police announced plans to sell off 22 of them.
Inquiries have been made from as far away as the United States and Canada, with a Doctor Who revival and an increase in businesses operating from the police boxes believed to be behind the unprecedented interest.
Sara Griffiths, property manager for Lothian and Borders Police, said that far more bids had been received for the current batch of the buildings than on the two previous occasions that the force had sold a stock of the blue boxes.
She said: “We’ve had far more bids than we were expecting. It’s certainly third time lucky.
“I think the Doctor Who thing has made a difference. Also, the media coverage and the internet means more people have heard about the sale.
“Some of them are in prime sites. Maybe people are seeing coffee shops operating out of them and are thinking ‘I could do that’.
“Retired cops might also have been interested. The boxes have a sentimental value.”
There were 86 of the boxes scattered around the Capital’s streets before 36 were sold in 1996. A further nine went into private ownership in 2007 before the latest batch were put up for sale.
Lothian and Borders Police had been spending more than £8000 annually in painting and maintaining their stock.
The 200-plus bids for the available boxes were received from around 130 bidders, with some making multiple offers for different boxes.
Some bidders specified which building they wanted to buy, while others said they would be happy to take any of the iconic structures.
The council, which is handling the sale on behalf of the police, was still processing the offers yesterday and said it was unable to reveal how much had been bid.
But Edinburgh auctioneer Charles Graham-Campbell, of Bonhams, estimated when the sale was announced that the boxes could fetch between £4000 and £6000.
Ms Griffiths added: “The bids will be analysed and we’ll see which ones are the best. We hope that within a couple of weeks we’ll be in a position to see what’s on the table.”
Successful bidders who want to operate commercially from the boxes will have to apply for licences from the council. The land on which they sit is not for sale.
Those who want to remove the structures and transform them into a unique piece of garden furniture will have to pay for their transportation themselves.
A series of conditions will come with ownership of one of the boxes, including rules over their colour.
They will have to be painted a different colour from their iconic police blue — even if they are on private property — over fears that members of the public would mistake them for real police boxes.
WHAT WHOVIANS CAN GET FOR £100,000
• 6666 K9 4-inch official collector’s figurine (£14.99)
• 7142 Sonic ballpoint pens (£13.99)
• 5885 Plush talking Daleks (£16.99)
• 2000 Inflatable Daleks (£49.95)
• 1538 Expanding Tardis play tents (£64.95)
• 3333 Doctor Who figures “The 10th Doctor” (David Tennant) in trenchcoats (£29.99)