Nationalised lender Northern Rock said it expects to make a profit during next year after reporting reduced half-year losses today.
The bank also confirmed it had received indicative offers from interested parties since Chancellor George Osborne announced in June his decision to put Northern Rock up for sale.
The lender reported underlying losses of £78.8 million in the six months to June, compared with losses of £140 million the previous year.
Northern Rock was nationalised in February 2008 after it collapsed amid the credit crisis, sparking the first run on a UK bank for 150 years.
Looking ahead, the company expects to be loss-making for the full year but with a "significantly improved position" compared with last year.
Ron Sandler, Northern's Government-appointed chairman, said: "The trading environment remains challenging and there is strong competition in the savings and mortgage markets."
He added: "The company expects to be trading profitably during the second half of 2012."
Northern Rock plc is being sold by UKFI, which was set up to manage the state's holding in banks bailed out during the crisis, such as Lloyds and RBS.
Virgin Money, Sir Richard Branson's banking business and JC Flowers, the US private equity investor, are understood to have tabled first-round bids for the bank last week.
A report at the weekend said the sale will deliver a loss for taxpayers of £400 million as both firms have indicated they could offer between £900 million and £1 billion, compared with the £1.4 billion pumped into the bank by the Government. It is thought that the Coventry and Yorkshire building societies both withdrew their interest on Friday.
Mr Sandler added: "We are pleased with the level of interest we have received, and will continue to explore the sale option over the coming months. In the meantime, it is business as usual."
The Government split Northern Rock in two at the start of 2010, forming a mortgage and savings bank called Northern Rock plc and Northern Rock Asset Management (NRAM) to house the more toxic loans.
NRAM last month reported a surge in pre-tax profits in the six months to June to £344.1 million, from £181.8 million last year.
UK Asset Resolution, the company which runs NRAM and Bradford & Bingley, last week said it had paid back another £1 billion to the government.
Northern Rock saw total income increase 42% in the period to £40.6 million, including net interest income of £29.8 million, compared to negative net interest of £48.4 million.
The improvement in net interest income reflected growth in the mortgage book, the bank said, as high quality mortgages grew and replaced lower-yielding assets.
Gross lending was £1.5 billion in the period, compared with £2 billion the previous year.