Private equity firm JC Flowers has approached Britain's Lloyds Banking Group about a bid for the TSB business that was split from the part state-owned bank earlier this month, the Sunday Telegraph said without citing sources.
Lloyds, which is now 32.7 percent-owned by the taxpayer after the government sold a 6 percent stake last week, has been working on a stock market listing for TSB next year.
The bank was required to sell more than 600 branches, which it has rebranded TSB, by European regulators as a penalty for receiving a 20 billion pound ($32 billion) government bailout in the 2008 financial crisis.
The Sunday Telegraph said the company had received interest from a number of private equity firms, including JC Flowers, for the branches.
The approaches were believed to be at an early stage, but were understood to have been taken seriously by Lloyds' management, the newspaper said.
It also said that New York-based private equity group AnaCap may have expressed interest in some form of trade sale.
A Lloyds spokesman told the newspaper that the group was pursuing a stock market listing but would be open to any offer that would give greater value or certainty.
Citigroup and JP Morgan are advising the group on options for TSB.
JC Flowers declined to comment to the newspaper.
Neither Lloyds nor JC Flowers were immediately available to comment on Sunday.