The UK lender is reported to have edged ahead of US private equity group Cerberus in the bidding for MBNA’s British credit card operation, City AM reports.
For Lloyds, it would mark the first acquisition since it was bailed out by taxpayers at the height of the financial crisis.
The Financial Times first reported that Lloyds had moved into pole position after Bank of America backed down on a crucial sticking point in negotiations.
Bank of America had originally refused to share the future costs of compensation in relation to mis-selling payment protection insurance (PPI).
But the US lender has now agreed to indemnify the new owner of the business if costs rise above a fixed cap.
MBNA has an 11 per cent market share of credit cards across the UK, giving it a loan book of around £7bn. The business is thought to be worth hundreds of millions of pounds.
Lloyds has been asked for comment. MBNA declined to comment.