John Stewart, the chief executive, said he had spoken to more than one insurance company with a view to entering into a joint venture, but had not yet entered detailed talks.
Mr Stewart said: "We could be interested in insurers. Anyone with good customer information we would be interested in talking to for a joint venture."
He dismissed reports that Woolwich is looking at a tie-up with Alliance & Leicester, which has indicated its interest in a merger. Talks with another retail bank or building society would run against the best corporate strategy for the Woolwich, he said.
"If that happened, the good news would be that we could cut costs. The bad news would be what happened with Halifax and the Leeds, or Abbey National and N&P. Did their market shares go up? For all sorts of different buying reasons, customers can walk."
Woolwich unveiled profits up 12.1 per cent to pounds 240m on the back of a jump in non-core businesses such as unit trusts and PEPs. Excluding PEPs set up to hold windfall shares, sales were up 36 per cent.
The society's market share of mortgage lending shrank to less than one- third of its normal level in the first half of 1998 to just 1.5 per cent. Much of this was due to the "post-conversion effect" where customers redeem mortgages after waiting for windfalls, but Mr Stewart conceded that the society might not rebuild its share to its historic level of 5.5 per cent.
While market share of lending did recover in the second quarter to more than 3 per cent, the Woolwich insists it will not sacrifice margins to chase market share.
Mr Stewart said the strategy was to diversify and improve income from non-core businesses, competing on service as much as price.