According to reports, the remaining bidders for the 318-strong branch portfolio, being sold by the government in an effort to enhance competition in the banking sector, are Santander, fellow Spanish group BBVA and National Australia Bank.
Virgin Money is looking to open a network of over 70 branches in the UK, having recently gained a banking licence through its acquisition of Somerset-based bank Church House Trust.
As part of long-term plans to offer savings and mortgage products, Virgin Money has increased its marketing activity and last month launched its sponsorship of the London Marathon.
Under pressure from the European Commission to improve competitiveness in the UK's financial services industry, the government has also earmarked RBS' insurance brand portfolio and 600 Lloyds Banking Group branches for sale.