Zurich Financial Services, one of the leading bidders for Royal Bank of Scotland's insurance arm, has decided to pull out of the running.
RBS is seeking to sell its insurance business, including its Direct Line and Churchill brands, for £7bn.
The sale is part of a number of steps the bank is taking to strengthen its balance sheet amid the credit crunch.
Zurich said it had decided to withdraw from any further discussions following a review of the business.
An RBS spokesperson declined to comment.
RBS is looking to shore up its finances to cover losses inflicted by the credit crunch.
Last month, it raised £12bn after selling shares to existing shareholders in a rights issue.
It has also sold off the UK's biggest train leasing firm, Angel Trains, for £3.6bn to a consortium.
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