The proposal is in early stage, although the bank’s management is seriously contemplating on the plan, as reported by the Sunday Telegraph.

Additionally, another private equity firm AnaCap has expressed interest in some form of trade sale, the news agency reported.

Lloyds, which is 32.7% owned by the British government, has been working for TSB’s stock market flotation in the middle of 2014, but failed to execute the plan.

Ultimately, the bank established TSB bank, with more than 600 branches, as per the agreement inked with the European regulators, when it received a financial package of £20bn during the financial crisis of 2008.

Most recently, the government divested 6% stake in the newly formed TSB at a transaction value at approximately £3.2bn ($5.1bn).

A Lloyds spokesman said, "We’re progressing towards an IPO of TSB next year but will consider any offers that would provide greater certainty or value to our shareholders."

Citigroup and JP Morgan are advising the British banking group on TSB.