Earlier, shares in the group plunged for a third day in a row amid funding fears, diving as much as 50%. The share price managed to recover to 7% down following the report before fluctuating between positive and negative territory..
Asked about the discussions, an HBOS spokesman declined to comment.
HBOS is also the UK's largest savings bank, with £258 billion of retail deposits and about 15 million savers.
Lloyds TSB, which does the bulk of its mortgage lending under its Cheltenham & Gloucester brand, is the UK's third biggest lender in terms of outstanding home loans. During 2007, the latest year for which figures are available, it wrote 8% of all mortgages in the UK.
The merger news fuelled a rollercoaster session for London's leading share index, which opened up, then quickly slumped to a 40 month-low before recovering back into the black.
Kevin Mountford, head of banking at moneysupermarket.com, said: "This is a time for nerves of steel. HBOS is fundamentally a sound institution with sufficient access to capital. Its weak share price bears no relation to the undoubted strength of the business. It is not only one of the largest retail deposit takers in the UK but also has a very diverse business. There is no need for consumers to panic, especially with the enhanced FSCS compensation limit of 100 per cent of the first £35,000 of savings with any one institution.
"More importantly, a shotgun marriage of HBOS and Lloyds TSB would not be in the best interests of British consumers. With the Santander/Abbey takeover of A&L confirmed today and building societies disappearing seemingly daily we are seeing a large reduction of competition and choice for consumers. It is the likes of A&L and Halifax that have been the most competitive for current accounts and many other products. HBOS can survive and prosper independently and in the medium to long term this is the better option for consumers."