According to Reuters reports, Richard Branson’s Virgin Money is in talks with Pitman over the role.
Pitman was lined up to chair Virgin Money if it had taken over Northern Rock in early 2008, but the lender was nationalised.
Last week Virgin appointed former RBS executive Finlay William-son as finance director, former Bradford & Bingley director of savings Ian Cornelius as banking director and HBOS head of legal for retail Marcus Ezekiel as commercial director.
Earlier this month Virgin Money agreed a deal to buy a small regional private bank Church House Trust as the platform for its retail banking launch.
Virgin Money would not comment on Pitman’s rumoured appointment.