Graham Beale, chief executive of Nationwide, which mounted a rescue takeover of Dunfermline Building Society in 2009, said: "Northern Rock is too small and has a considerable overlap with our branches."
Mark Rennison, Nationwide's finance director, pouring cold water on a deal with Lloyds, said: "No. We are not interested in that transaction. It's very sizeable compared with the 700-plus branches we have now.
"It would be a complicated deal, it comes without systems infrastructure. The delivery risks would be high."
The remarks came as the mutual posted a profit of 276 million in the year to 4 April, aided by a 35 per cent fall in sour loans to 359 million and a 1.6 billion rise in retail deposits. The figures also benefited from a cost- cutting drive to save some 5m.
Rennison said the Dunfermline society integration was now completed, including the already-announced changes making the Dunfermline HQ the hub of the group's regional business, involving the creation of more than 100 jobs.
"That was a sign of our commitment to the (Scottish] operation. The integration has gone well," Rennison said.
The finance director said Nationwide was sticking to its earlier forecast of a stagnant housing market for the rest of 2011, "with little movement in either direction on house prices".
Rennison said the society was continuing to see borrowers pay down their mortgages early in the low interest rate climate, while, despite the difficult economic backdrop, one in four of Nationwide's home loans in the period was for first-time buyers. Nationwide reported gross mortgage lending of 12.8bn, a market share of 9.5 per cent.
Rennison added that consumers were concerned about the impact of the government's austerity programme to cut the public debt, but that "what's to come is already priced into consumer confidence".
Nationwide revealed that it had earmarked 16m to cover compensation claims for the mis-selling of payment protection insurance, which analysts said compared very favourably with the several billions of pounds of provisions on the issue announced by banks recently.
"We had a far less significant share of that market and came out of it in 2007," Rennison said. "We are a mutual and not a profit maximisation institution. We like to sell products responsibly."
On the interest rates versus inflation debate, the finance director admitted the Bank of England had "a difficult balancing act" between curbing price rises and not constricting economic recovery.He said Nationwide believed rates, currently at 0.5 per cent, would go to 1 per cent by the first quarter of 2012, and 2.5 per cent by Q1, 2013.
The group revealed that its financial strength had also improved, with the core tier one ratio moving up to 12.5 per cent from 12.2 per cent in the latest trading period.