It is understood the entrepreneur could pull the flotation if the shares are not priced within the proposed range of 235p to 285p.
According to reports, Mr Branson has been advised that he could make more money through a debt refinancing of Virgin Mobile and keeping the company private. Virgin Mobile announced plans to float three weeks ago in a move that could value the group at £960 million. Conditional dealings were due to begin this week and would mark the first flotation by part of the Virgin empire in 18 years.
However, it is believed that the minimum price of the proposed price range will not be reached.
One executive at financial betting firm Cantor Index was quoted as saying: "the closer to the bottom end of the range you get, the more attractive it is for Branson to keep Virgin Mobile private."
Instead of pulling the flotation, the company could choose to slash the number of shares on offer to investors, the newspaper added.
This would increase competition among institutions for the stock and protect the price level.
Branson is expected to make a final decision tomorrow night, before the scheduled debut on Wednesday. Virgin Group hopes to raise more than £250m from the listing. The operation was founded five years ago and differs from rivals such as Vodafone and MMO2 as a "virtual operator" which uses the network of T-Mobile. It has more than four million customers and employs 1,400 staff at three sites.
The reported lacklustre response to the Virgin float reflects the current mood of the market.
Investors have been asked to back a number of new share offers in the last month, including advertising group M&C Saatchi and Branston Pickle-to-Typhoo Tea company Premier Foods.