The shares climbed to $3.60 in early trading, according to the Guardian.
Chances of a sale seemed unlikely until the news of the fresh bids, with many banks ruling themselves out of the running and Royal Bank of Scotland and Barclays locked in a bidding war for ABN AMRO.
There has also been speculation earlier in the week that a consortium of hedge funds was interested in bidding for the bank, with the intentions of breaking up the lender and selling the existing mortgages.
In a statement Northern Rock, said: "The company has received a number of approaches regarding a variety of potential transactions, including the possibility of an offer being made for the company, although no price has been referred to.
"The company is in preliminary discussions with selected parties but emphasises that there can be no certainty as to the outcome of such discussions."