NBNK has made a revised offer to Lloyds Banking Group to buy the 632 branches it was due to sell to Co-operative Group.
The sale of the branches, known as Project Verde, was enforced so the bank would comply with European Union rules on state aid.
In a statement to the market, it said the updated proposal offers an "alternative demerger structure" to Lloyds - giving its shareholders, including 41% held by the UK government, the option of getting cash directly and/or receiving shares in what would be the country's only "major, listed organisation solely dedicated to retail and SME banking".
NBNK chairman Lord Levene said: "NBNK offers none of the downsides to Lloyds of a standalone IPO. We have the right board, management, strategy and experience to run and grow a large scale banking operation and achieve our plans for Verde. Our shareholders are strongly supportive of our objectives."
NBNK chief executive Gary Hoffman added: "Our objective is to create a new, large challenger bank and brand that will shake-up UK high street banking, operating in the interests of customers.
"I believe we have tabled a compelling proposition that will invigorate competition, provide jobs and is the right solution for taxpayers."
The business said it had been in close contact with the Financial Services Authority throughout the bid process.
Cautious, Balanced & Dynamic Growth
Cowardly, boring or sensible
Latest news and analysis
‘Most significant’ upgrade since launch
Changes happening over coming months