Northern Rock shares surged 11.6% on Wednesday following Tuesday's announcement that the troubled bank is in takeover talks.
The bank said it was "in preliminary discussions with selected parties", but warned there was no guarantee that the talks would lead to a deal.
Northern Rock also confirmed it would not pay its planned dividend - worth £59m - to shareholders next month.
Northern Rock shares closed up 18.9 pence at 182.0p.
First news that the dividend payments would be withheld came from BBC business editor Robert Peston.
He said the bank had come under intense pressure from the Financial Services Authority (FSA) and the Treasury not to make the payment.
Northern Rock also said it was in talks with people who wanted to buy some or all of its business.
"The company has received a number of approaches regarding a variety of potential transactions," it said in a statement to the London Stock Exchange.
"This includes the possibility of an offer being made for the company although no price has been referred to," it added.
Analysts were encouraged by the news, but warned that the outcome for investors was still far from clear.
"In view of the range of what we consider to be possible values for the shares, from zero to 357 pence, the final outcome for equity shareholders remains opaque," Robert Sage at Bear Stearns said in a note.
Northern Rock's interim dividend payment was due on 26 October, but the bank said it "would not be appropriate" to pay shareholders until it was sure about its eventual ownership and structure.
The 14.2 pence per share payment was announced before its problems emerged.
"The Treasury was deeply unhappy about Northern Rock paying a dividend at a time when the government has been forced to underwrite all deposits and loans to Northern Rock," our business editor said.
Two weeks ago, it applied to the Bank of England for emergency funding after being unable to borrow money in the wholesale money markets at an affordable rate of interest to cover its home loans.
This is the way Northern Rock typically operates its business, but the turmoil over the summer in the credit markets meant it was stuck for short-term cash.
Repeated reassurances from Northern Rock that it was solvent failed to quell a run on the bank.
But even after the government pledged to guarantee all Northern Rock deposits held in accounts as of midnight, 19 September, the bank's share price has continued to drop, so that about 70% has been wiped off its value since the beginning of the month.
The cancellation of the dividend is another blow for shareholders, who have now joined forces in an action group to promote their interests.
The group has been set up by the UK Shareholders Association (UKSA), which says "many shareholders were persuaded to invest in shares in the company in recent months based on the apparent strength of the business when in reality the company was in great financial difficulty".