The aim of the project is to build a global monument that will stimulate people to think beyond the normal human concept of time, as measured by hours and days, by encouraging them to think in terms of centuries and millennia.
Artists and computer engineers who have set up an organisation called the Long Now Foundation to build the clock, believe politicians are the key people to win over to the idea of a 10,000-year timepiece given their prediliction for thinking in the short-term.
A prototype clock standing seven feet tall will be completed in the next few weeks and if the foundation secures the funding it is seeking, the full-scale version standing up to 80 feet tall will be built at a dry, desert site somewhere in world.
Using simple mechanical levers and devices that could be mended with Bronze Age technology - in case modern civilisation is destroyed - the clock is designed to tick once a day, move its hands once a year, bong once a century and do something spectacular once every thousand years.
"Most of the workings will be buried below ground as it needs to be fairly well protected, but the moving parts on its face will be visible," said Alexander Rose, director of the Long Now Foundation in San Francisco.
The clock is the brainchild of a computer scientist, Danny Hillis, and Stewart Brand, an author who is writing a book on the project to be published later this year. "We've got an invitation to debut it at Davos. It is the perfect place to get world leaders and corporate leaders and so on thinking in 10,000 year terms," Mr Brand said.
Brian Eno, the British musician and artist, who is also a board member of the foundation, came up with the name of Long Now after moving to New York and being made to realise that the city's concept of "now" was even more short term than in Britain.
"The idea is that you sort of move in the now and feel a responsibility for what happens in the now; if you can push the now out past your own lifetime in a couple of directions, that's good," Mr Brand said.
The 10,000-year clock will be built out of tungsten and steel which in a dry climate should last for many thousands of years. A giant torsion pendulum will drive the clock and it will use the sun's position at midday to ensure that it keeps the right time.
Sites in Egypt, Jersusalem, China and a desert mountain in Nevada are being considered.