The company's president said he was in talks with six candidates from different countries who want to be flown on Mir for money.
Multimillionaire businessman Dennis Tito has made enough money to afford any holiday destination and he has chosen the world's most exclusive hotel: the Mir space station.
Mr Tito, the founder of Wilshire Associates, a Santa Monica-based investment consultancy that manages assets worth $10bn, is currently negotiating the price of his ticket. A week's stay will cost him many millions of dollars.
If he passes all the tests, Mr Tito, 59, is likely to become the first tourist in space early next year.
Mir is not, however, what you would call five star accommodation. It is extremely cramped and you have to share the limited space with two other people.
Right stuff
Things can also get a little heated on the 14-year-old space platform at times. Mir has been the site of a series of accidents and breakdowns, including a terrifying fire and a near-fatal collision with a cargo ship in 1997. Mr Tito, though, is undaunted.
"I am optimistic that I do have the right stuff to make this flight."
He appears to be the perfect candidate. Before moving into a highly successful business career, Dennis Tito was a rocket scientist at the US space agency Nasa's Jet Propulsion Laboratory in Pasadena, California.
He worked on flight trajectories for spacecraft to Mars and Venus.
Six would-be cosmonauts
MirCorp, an Amsterdam-based firm, now owns the commercial rights to exploit the Russian space station. It plans to transform the platform into a commercial centre for media, entertainment and research.
A team of cosmonauts returned to Earth from Mir last Friday after a mission partially funded by MirCorp.
The company's president said he was in talks with six candidates from different countries who want to be flown on Mir for money.
"Mr Tito represents the first of a generation of people who has the means and the dream," said Jeffrey Manber.
"He will be going through months of training. There is no sacrifice of safety. We all understand the steps necessary to send a person into space."
He said investors were showing increasing interest in the company's plans to open the first internet portal in space, which would be capable of relaying live images of the Earth surface, and its plans to produce highly pure medicines and alloys.
Flight schedule
MirCorp's board of directors will meet on 17 July to review the decision on Mr Tito's flight. At the moment, it is scheduled for the first half of 2001.
And before he goes into orbit, another team of cosmonauts will need to fly to the space station to resuscitate the platform after a period of unmanned flight.
No specific date for this mission has been set either.
Dennis Tito will be accompanied to Mir by two Russian cosmonauts. It is not clear what he would do for the week he spends on the space station. Although his previous experience in space research could be useful in any scientific experiment.
On the other hand, he may just want to enjoy the view.
"I want to experience space. That is my first desire," Mr Tito said. "I want to be able to assist the crew where I can, not be a burden to the crew."