But it has said it is open to talks with other parties and Arnold said he was optimistic his proposal better meets the needs of government, shareholders and other stakeholders.
"The government has indicated its complete openness to any proposals that address the issues and the needs ... (we) can repay the loan while treating shareholders very well," he said.
"Our proposal is simpler, smoother and quicker," he added, saying it was based on stabilising the bank, bringing in new management and then developing the company as "a strong, independent brand" -- keeping the Northern Rock name.
Olivant, the group headed by Arnold, the former boss of British bank Abbey, said under its proposal Northern Rock would quickly repay between 10 billion and 15 billion pounds of Bank of England (BoE) loans and repay the balance by the end of 2009.
The Virgin group has said it would immediately repay 11 billion pounds of the BoE loans.
"There's a pretty finite amount that can be raised in today's market for this company with its assets, and the range right now is 10-15 billion (pounds)," Arnold said.
He declined to say who would fund this, but said a lot of banks are involved across the different offers but financing could not be committed until details of a rescue are confirmed.
U.S. private equity firm Cerberus remains interested in leading a consortium to buy Northern Rock, a person familiar with the matter said on Friday.
Olivant said it planned for Northern Rock to raise between 450 million and 650 million pounds through a rights issue at near the prevailing market price. Olivant would subscribe for further shares worth about 150 million pounds, giving it a stake of about 15 percent.
The company said it had non-binding support from shareholders owning 23 percent of Northern Rock to take up their share of the rights issue and to sub-underwrite approximately 440 million pounds of the issue near the current market price.
Hedge fund RAB Capital, the second-biggest shareholder with a 6.7 percent stake, said it backed Olivant as its proposal was more attractive for shareholders. Northern Rock remains a viable business with the right strategy and management, RAB said.
SRM Capital, a hedge fund holding a 9 percent stake, is reported to also back Olivant but could not be reached. Small investors are estimated to hold about a quarter of Northern Rock's shares, and Olivant said it had support from retail shareholder groups.
"Of all the potential offers which have been described in the public domain, that from Olivant seems to align most closely with our aims," the Northern Rock Small Shareholders Group said.
"It is essentially an injection of leadership in the context of a shareholder-led solution."
By 1250 GMT Northern Rock shares were up 1.8 percent at 104.9 pence, valuing the bank at 440 million pounds.
Olivant will also be issued high-premium warrants over 7 percent of the enlarged company and the Bank of England will be issued warrants on the same terms over 5 percent of the capital.
Buyout firm J.C. Flowers withdrew from the auction as it had found it "impossible" to construct a deal that would deliver required value for Northern Rock shareholders alongside its own profitability criteria, a person familiar with the matter said.
Flowers remained interested in Northern Rock and it could re-enter talks if the auction process stumbles, he said. That would be based on a proposal made in mid-November, which included an offer to shareholders at a "nominal value."