Currently attached to the Lord Provost's Lexus, the S0 registration was created after Edinburgh's civic leader missed out on Scotland's first number plate – S1 – at the turn of the 20th century.
Just weeks after that plate sold for nearly £400,000 at auction, the council is under pressure to sell the S0 number plate to raise funds for local services.
Experts today said such a sale could fetch up to £500,000, but Lord Provost George Grubb has insisted he will hold on to S0, saying it belongs to the city.
If it were to be sold, the council would have enough money to re-instate recently axed bus routes, or bring back popular holiday programmes for school children.
Tory councillor Jason Rust said: "In light of the staggering sale price achieved for S1, and given the dire economic circumstances the council finds itself in, serious consideration should be given to obtaining a valuation of the S0 number with a view to the registration being auctioned.
When number plates were introduced in 1903, Scotland was assigned the prefix S.
It is thought the first plate, S1, would traditionally have been destined for the Lord Provost's car, but city fathers were too slow off the mark. Instead, it was bought by Sir John HA MacDonald, a motoring pioneer who was president of the Scottish Automobile Club.
What happened next is a mystery, but at some point the Ministry of Transport agreed to establish the S0 plate.
Collectibles specialist Jon Baddeley, a director at auction house Bonhams, today said the S0 registration could fetch as much as £500,000.
The auctioneer, who has valued items for the BBC Antiques Roadshow TV programme, said: "I think, with M1 recently fetching £330,000 and S1 going for just shy of £400,000, this has got to be in that range and maybe more.
"A letter with a zero makes it even rarer than S1."
However, a council source said: "This is a ridiculous idea. It's akin to the Lord Provost selling his chain. This number plate should not just stay in the city, but stay with the council."
A spokesman for the Lord Provost added: "The S0 plate belongs to the city and has done for a very long time – it's not for sale and won't be put on sale."
At number plate auctions, buyers purchase the right to use the registration, rather than the physical plate.