Aviva is among a number of firms considering bidding after the Co-op put the division up for sale last month to raise cash to plug a capital shortfall - which is threatening its swoop for 632 Lloyds Banking Group branches, according to The Sunday Times.
The Co-op has already sold its life insurance and asset management arm to Royal London for £219 million to boost its balance sheet as City regulators put lenders under pressure to address a £25 billion combined capital hole.
It is thought that Aviva is among a number of potential bidders, also including Ageas, the UK arm of Belgian financial services group Fortis, and private equity entrepreneur Edmund Truell.
But such a move would be controversial for Norwich-based Aviva, which has been shrinking not expanding in recent years. Only last week it revealed plans for another 2,000 job cuts across its UK, European and Asian workforce.
Under new boss Mark Wilson, Aviva is undergoing a major restructuring which last year saw £275 million of annual cost savings and a £1.1 billion deal to exit US life and pensions. It reported a loss after tax of £3 billion in annual results last month and shocked investors with a 44% cut in its full-year dividend to 9p a share.
The Co-op is believed to have appointed Deutsche Bank to sell its general insurance business, which provides cover for cars, homes and pets. It is under scrutiny amid fears that its takeover of Lloyds branches is on the rocks and after its banking division racked up annual losses of £662 million.
The Co-op blamed the big banking loss on loan impairments on non-core operations mainly relating to its 2009 acquisition of Britannia and a further provision of £150 million to cover payment protection mis-selling. However, its core banking business still saw profits fall to £120 million, from £173 million a year ago.
The Co-op's deal with Lloyds is worth up to £750 million and will boost its branch network to nearly 1,000, adding another 4.8 million customers to its existing 6.5 million base.