The two customers who already have booked flights may ride together on mission or be on separate excursions, the first of which could occur as early as 2017, Shelley said.
"Over the course of the next three years, we will evaluate whether those two customers will be on the first mission or if they will decide to go on the first and the second and we'll get some other customers to go on as well," Shelley told Discovery News.
NEWS: Singer Sarah Brightman Headed to Orbit?
"We're talking to the Russians about a series of missions, not just a one-off," he added.
The trips could include a short stopover at the International Space Station, a research laboratory operated by 15 nations that flies about 260 miles above Earth. Space Adventures arranges for well-heeled space aficionados to fly there too.
Beginning with California businessman Dennis Tito's trip in 2001, the company has arranged eight privately funded trips to the station, including two visits by Microsoft co-founder Charles Simonyi. British singer Sarah Brightman is due to fly next year, possibly followed by Google co-founder Sergey Brin in 2017, Shelley said.