According to the Financial Times, Virgin Money plans to make a formal bid in July for the 600 locations the bank is to sell.
Speaking to the newspaper, the entrepreneur said of the possible purchase: "This can happen quickly and smoothly. We are a serious bidder and can give the government what it wants through competition."
According to the news outlet new entrants such as Virgin Money are being encouraged into the banking sector by MPs who would like to see the dominance of the nation's main providers broken up.
MP Andrea Leadsom suggested there should be dozens of banks in operation, rather than just four or five.
Lloyds Banking Group chairman Sir Win Bischoff recently revealed the lender was contemplating whether or not pay should be affected for those responsible for the losses incurred through the payment protection insurance debacle.
By Gary Cooper