The company, Space Adventures, has signed a preliminary contract with the future tourist, whose name has not been disclosed.
The tourist-to-be is now due to sign a contract with the Russian space agency before year end, an agency official told ITAR-TASS on condition of anonymity.
The tourist "is not Russian, but he is a national of one of the countries involved in the ISS project," the official said.
There are 16 partner countries in the ISS project, including the United States, Russia, the member states of the European Space Agency (ESA), Canada and Japan.
Space Adventures said last month it had drawn up a list of 10 candidates interested in boarding a Russian rocket and blasting off for the ISS, after Rosaviokosmos, the Russian space agency, announced it planned to carry two more tourists to the space station in 2004-2005.
Russia had tasked Space Adventures with finding fit -- and rich -- candidates for the trips.
The asking price for a 10-day visit to the ISS is around 20 million dollars (17.2 million euros), a sum only two space tourists -- Californian businessman Dennis Tito and South Africa Internet millionaire Mark Shuttleworth -- have so far been able to afford.
Trips scheduled by US pop star Lance Bass, from the boy band 'N Sync, and former NASA official Lori Garver was called off after they were unable to pay.
Russia and the United States, the major partners in the ISS project, have clashed in the past over Moscow's keenness to raise money for its cash-strapped space program by selling tourist tickets to the ISS.
In February, Russia announced the temporary suspension of space tourism flights after the US shuttle Columbia disintegrated on its way back to earth from the ISS.
The tragedy forced the United States to rely completely on Russian craft to ferry crew and supplies to the ISS.