The idea is to build a global monument that will stimulate people to think beyond the normal concept of time, as measured by hours and days, by encouraging them to think in centuries and millennia.
Artists and computer engineers who set up 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 predilection for thinking in the short term.
Brian Eno, the British musician and artist who is a board member, came up with the name of Long Now after moving to New York and realising that the city's concept of "now" was even more short term than in Britain.
A prototype clock standing seven feet tall will be completed in the next few weeks and if the foundation secures funding, the full-scale version standing up to 80 feet tall will be built at a dry, desert site.
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. "Davos is the perfect place to get world leaders and corporate leaders and so on thinking in 10,000-year terms," Mr Brand said.
The clock will be built out of tungsten and steel which in a dry climate should last for thousands of years. A giant torsion pendulum will drive the clock and it will use the sun's position at midday to keep the right time.