In an interview with CNBC, Branson said his company was "more than tantalisingly close" to its first landmark flight beyond Earth's atmosphere, stating: "we should be in space within weeks, not months".
"And then we will be in space with myself in months and not years".
One ticket on the Virgin Galactic project costs around $250,000.
Virgin Galactic is now in a tight race with Jeff Bezos-owned Blue Origin to launch the first space passenger flight which will bring paying passengers within the boundaries of Earth's atmosphere and space known as the Karman line.
THE waiting list to travel to outer space on board Virgin Galactic's new spaceships first closed four years ago, but the demand to become a space traveller has far from waned.
It was the first since a fatal crash in 2014, which delayed the firm's plans.
Musk also dreamed up the idea of an ultra-high speed transportation system called Hyperloop, as well as a space tourism business called SpaceX.
Despite the recent successful test flight after this tragic incident, it remains hard to believe that they will launch successfully so soon. It performed powered test flights in April and May. The company is developing commercial spacecraft and aims to provide suborbital spaceflights to space tourists and suborbital launches for space science missions.
Sir Richard conceded earlier this year that the number of spurious claims he has made about Virgin Galactic flight dates was "embarrassing".
Last we heard of VSS Unity, it conducted a flight test that took it into the Mesosphere of the planet, 170,800 feet above sea level. Tourists will be able to cross the imaginary boundary where space begins, or the line of the Pocket at an altitude of 100 kilometers.
The reusable New Shepard rocket and spacecraft is meant to carry up to six space tourists, researchers and/or experiments on brief suborbital flights, the company has said.