Norwich Union has been tipped to win the AXA Direct book after putting in a bid described as "head and shoulders" above the competition.
The strength of the estimated £27m offer, at least 20% higher than any other bidder, forced AXA to by-pass the second stage process and go straight to exclusivity. It effectively knocked out the other major bidders, including esure, Hastings Direct and Rubicon.
A market source said: "The book attracted a lot more attention than most people were banking on, but one bid was head and shoulders above the rest. The company was biting off AXA's hand to buy the business."
The AXA Direct book consists of approximately 80,000 home and 210,000 motor policies. According to sources it was running on a loss ratio of around 80%.
Although policy numbers were lower than some buyers expected, the business attracted enough interest to force AXA to put it on the market after originally saying it would put it into run-off.
A market source said: "The risk portfolio and socio-economic profile of the customer base makes the book highly attractive."
But by offering up to £5m more than the nearest competitor, the bid has raised fears of a price war, as insurers fight for market share.
A source said: "That sort of price is crazy. There is no way in a reasonable market that the business is worth that.
"Paying that sort of money can only add pressure on motor premiums in an already shaky market."
Both AXA and Norwich Union declined to comment.