Citigroup has held talks with trade buyers and a private equity firm over the potential sale, which would see it virtually pull out of the UK retail banking market altogether, a Sunday newspaper reported.
It bought Derby-based Egg – the world's largest internet bank – in early 2007 before the credit crunch and recession sent markets reeling.
But Egg has been hit by the recession as well as online competition and posted a loss of 106m in the six months to last June, it was reported.
Citigroup, meanwhile, is shrinking its balance sheet to concentrate on the US after a huge bail-out put a third of the business into public ownership. It posted losses of $1.6bn (980m) in 2009.
Egg, which has around 1,800 staff and two million customers, was set up by Prudential in 1998.
After failing to sell the business, the Pru took full control of Egg in 2005 by buying out minority shareholders in a deal that valued the internet bank at more than 900m. But following two years of disappointing performances Pru agreed to sell the business in January 2007.
No-one from Citigroup was unavailable for comment last night.