Speaking to CNBC in Singapore, the billionaire Virgin founder said the company was "more than tantalizingly close" to launching its first mission to space, and that he himself hoped to briefly leave Earth within "months not years".
The current asking price for a short trip to the lower edges of space costs around £200,000 to book through Virgin Galactic, although Branson says that once his fleet is fully running that could fall to around £40,000 within a decade or so.
But while Sir Richard believes Musk is "doing fantastically well" in getting cargo into space - including his own auto - the real tussle is between the Virgin boss and Bezos.
Virgin Galactic, which is charging £190,000 ($250,000) for a spot on one of its commercial flights, has previously said it would send passengers to space in 2019. The original expected launch date was April 2018.
The CEO said he's been working out and undergoing astronaut training. His training includes extensive tennis and cycling. In 2014, an early version of a Virgin Galactic spacecraft pulled apart and crashed during a test flight over the Mojave, killing co-pilot Michael Alsbury. The next phase of testing will see the rockets test their endurance and range, hopefully soon reaching the limits of space.
That said, there appear to be some serious players in this nascent market, the most prominent of which, aside from Virgin Galactic, are Blue Origin, led by Amazon CEO Jeff Bezos, and SpaceX, run by Elon Musk.
Needless to say, Musk is facing legal action for the former, and has received a $20 million fine from the Securities and Exchange Commission for the latter.
The 68-year old added: "We should be in space within weeks, not months".
According to the businessman, "The market for people who would love to become astronauts and go to space is huge".
The next logical step is reaching space in the craft.
The claims by Sir Richard follow rival Elon Musk's SpaceX announcement it has its first private passenger it plans to fly to the moon in 2023. "It is up to us to produce as many spaceships as we can to cater with that demand". "I love life, I love people, I love learning, and I love the variety of what I do", said the man who describes himself on his Twitter profile as a "tie-loathing adventurer, philanthropist and troublemaker who believes in turning ideas into reality".