Branson joined forces with Brawn GP before the Australian Grand Prix
Sir Richard Branson has made Brawn GP an offer to become their main sponsor.
Branson's Virgin Group joined forces with the Formula 1 team just before the Australian Grand Prix and early success has seen Brawn's popularity rise.
"At the moment we are negotiating and we may or may not end up doing a full branding exercise," said Branson.
"If someone comes in and pays a silly price we will bow out gracefully. At the moment we've made an offer we feel we can afford."
Brawn GP drivers Jenson Button and Rubens Barrichello secured a one-two at the season-opener in Melbourne barely 24 hours after Branson confirmed a "substantial sponsorship" deal for the former Honda team, owned by Ross Brawn.
Button also won in Malaysia and was third in China to top of the drivers' standings ahead of Sunday's Bahrain Grand Prix, ensuring the Brackley-based team have suddenly become a hot ticket.
"The team have become very popular since the beginning of the season," said Branson. "If we don't do it (become the principal sponsor) we will obviously be the sponsor for this year and would be delighted with the way it has gone, and if we end up doing it, even better. Let's see how it goes.
Team principal Brawn confirmed discussions were still ongoing, adding: "We are looking to try and develop a bigger, longer-term relationship.
"It is understanding what they want and what we want. In this particular (financial) environment, any team is looking for medium-term commitments, so it would be nice to have our principal funding in place for the next few years."
Branson was in the paddock at the Sakhir circuit to promote his Virgin Galactic programme which Barrichello and Niki Lauda have already subscribed too, paying $200,000 (£136,000) for their ticket.
Branson revealed former three-time F1 champion Lauda, a fully-trained pilot after owning his own airline, will also learn to fly the Virgin Galactic plane.
"The mothership is now completed, finished and flying and doing its testing, whilst the spaceship will be completed at the end of the year," added Branson.
"Then there will be another 18 months of testing. We will do more tests than NASA have flown missions before we take people up.
"Myself and my family will then go up on the first flight, and Niki when he is finished, will be capable of flying both."
Lauda, 60, said: "I have been a professional pilot for many years, and although I've flown Boeing and Airbuses, my only dream was to fly the Space Shuttle.
"I was always looking at that, but that was impossible because the Americans do that, so when I saw this project I was the first knocking on the door."
Branson is planning to build one of three spaceports - the other two in America and Australasia - in either Bahrain, Qatar, Abu Dhabi or Saudi Arabia.