Chancellor George Osborne announced earlier this week that the state-owned business would be sold back to the private sector.
This morning the Virgin boss : "Northern Rock put on block by UK Government. Virgin Money to look at figures to see if we can make them and Lloyds Branches stack up."
Virgin has already expressed an interest in buying Lloyds Banking branches for sale, due to a ruling by European competition regulators.
In his annual Mansion House speech to the City this week, the chancellor said he hoped to find a buyer for Northern Rock by the end of the year. The sale is expected to raise £1bn for the Treasury. Northern Rock was nationalised in 2008, after the first run on a UK bank for around 150 years.
Yorkshire Building Society, the second largest building society in the UK, has also expressed an interest in bidding, with chief executive Iain Cornish stating it would be a "credible bidder".
Virgin Money gained a banking licence in January 2010 through the acquisition of Somerset-based private bank Church House Trust.
Last month, Virgin Money announced on high streets in London, Edinburgh, Norwich and Manchester.
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