Investment group Resolution is in talks with shareholders at Bradford & Bingley (B&B) about a plan to pump £400m ($787m) into the troubled UK lender.
Resolution said the proposal was part of a wider £2bn scheme to breathe life into the UK's smaller banks and lenders hit by the credit crunch.
But B&B rejected the plan, claiming it would mean Resolution in effect taking control of the company.
The bank has already announced a rights issue and an investment from a US firm.
B&B shares rose 14% to 75 pence in early trading.
Under Resolution's plan, the group would invest £2bn in the sector over the next two years, bringing together banks and lenders hit by the credit turmoil to create a "new, larger and stronger bank".
The company said some of B&B's key investors were interested in its plan to shake up the UK's smaller banks. It aims to table a formal proposal by 4 July.
Financier Clive Cowdery, who runs Resolution, already owns a 2.9% stake in B&B.
But the UK lender said it would push ahead with a planned $507m rights issue and investment by US private equity firm Texas Pacific Group (TPG), announced earlier this month.
TPG aims to buy a 23% stake in the UK bank for £179m.
B&B will give shareholders a chance to vote on its plan on 7 July.
The UK's biggest buy-to-let lender has been hit hard by the freeze in the credit markets.
Last week, it raised its mortgage rates for new borrowers because of the increased cost of raising funds in the financial markets.
Bradford & Bingley shocked investors earlier this month with a profit warning, which it blamed on increasing arrears among its borrowers.
As a result, the company has been forced to cut the value of its rights issue.