A ticket into space on board a Virgin Galactic flight will be a costly £192,000 ($250,000) - but "ultimately" he would expect it to fall to £31,000 ($40,000) within a decade.
When the plane reaches space, the vessel will detach and propel itself higher into space before both return to Earth - albeit at different times.
Virgin Galactic's disaster-struck space tourism programme is apparently nearing final launch readiness, with Branson telling USA news site CNBC that: "We should be in space within weeks, not months".
He said: "They believe in Elon Musk".
Virgin Galactic's first paying customers will see a hefty ticket price, however.
He said the firm would be taking people into space "not too long after" that. The company is developing commercial spacecraft and aims to provide suborbital spaceflights to space tourists and suborbital launches for space science missions.
'You know, it's important he's got to find time for himself, ' the 68-year-old said.
He responded: 'I think he maybe needs to learn the art of delegation.
'He's got to find time for his health and for his family. "And then we will be in space with myself in months and not years", he said. He's a wonderfully creative person but he shouldn't be getting very little sleep.
The feat would mark a milestone for the company which is in a race against Jeff Bezos' Blue Origin and Elon Musk's SpaceX to offer space flights to wealthy would-be astronauts. The upper atmosphere is generally regarded to give way to space at an altitude of 62 miles (100km), almost twice the altitude achieved in the July test flight.
"We should be in space within weeks, not months".
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.
Sir Richard conceded earlier this year that the number of spurious claims he has made about Virgin Galactic flight dates was "embarrassing".