Branson reportedly met Lloyds chief executive Antonio Horta-Osorio on Tuesday and is set to bid for the branches LBG is being forced to sell by the European competition commission.
Speaking to the Financial Times Branson said: “This can happen quickly and smoothly. We are a serious bidder and can give the government what it wants through competition.”
If Virgin Money is successful it would make it the sixth biggest bank in the UK.
It is understood that Virgin Money chief executive Jayne-Anne Gadhia has held talks with various interested investors and is confident of having raised £3bn by the end of July.
Virgin Money failed in previous bids to acquire Northern Rock in 2007 and then 318 Royal Bank of Scotland branches in 2010.
National Australia Bank, which owns Clydesdale and Yorkshire Banks, and NBNK, the investment vehicle set up by Lord Levene, chairman of the Lloyds of London insurance market, are also thought to be interested in the LBG branches.