Shares in Northern Rock fell by more than 25% on Tuesday, before recovering to stand 7% down, as uncertainty about whether it would be bought continued.
More bids for Northern Rock are thought to be expected soon
Its shares cost £12 each in February but have fallen steeply this week - to close at 97 pence on Tuesday.
The bank has said offers from suitors were below Friday's closing price.
Meanwhile the BBC has learned that US buyout firm JC Flowers submitted an offer that included an offer to Rock shareholders at a "nominal value".
Trading in Northern Rock shares was briefly halted on Tuesday.
The Bank of England has lent it more than £24bn in emergency funding, a move defended by Chancellor Alistair Darling in the Commons on Monday.
Both the Conservatives and the Liberal Democrats have criticised the loans.
Mr Darling had told the Commons in a statement that the loan move was "right" to give the bank time to assess its "strategic options".
In addition, the government has pledged to guarantee the £16bn worth of savings deposits held by Northern Rock customers.
Those who have so far submitted proposals for Northern Rock include a consortium led by Sir Richard Branson's Virgin and another fornted by private equity group Cerberus.
Northern Rock, which has around 6,000 staff, has said it expects to receive further expressions of interest over the "next few days".
But the company has said the proposals received so far from potential investors were "materially below" the stricken bank's share price.
Northern Rock was forced to seek emergency funding from the Bank of England in September after the jamming up of world credit markets wrecked its business model.
The government has a number of options when it comes to Northern Rock's future - it could let the bank go into receivership, seek a private buyer, or take it over itself.
Meanwhile, Northern Rock says it continues to be engaged in discussions with refinancing companies to explore refinancing "or reorganisation solutions for the company".
On Wednesday banking union Unite will launch a charter, designed to ensure its members are protected in any Northern Rock sell off.
The union represents 4,500 Northern Rock staff in the north-east of England.
Its deputy leader Graham Goddard said members were "worried at this stage about what's going to happen to the work, what's going to happen to the agreements, terms and conditions, pension arrangements and ultimately the jobs in the North East".
Meanwhile, former Conservative Chancellor, Kenneth Clarke, said the government had to make a decision on the bank's future in the next few days, with nationalisation a possibility.
"This is all going nowhere fast it seems to me and Alastair [Darling] has got to insist that the taxpayers' money is protected and is recovered as rapidly as possible and that narrows the options."