The deficit, revealed in the Financial Times, was far higher than the£477 million the trustees reported in October last year when Sainsbury's made a large cash injection to the scheme.
The reason for the increase is because of a likely change in investment policy for the pension scheme were the business to be sold.
The trustees are said to be concerned that if private equity houses took control of the company they would be tempted not to make any further contributions to the scheme, which would result in the deficit widening to£3 billion.
Sources close to a potential deal between a group of private equity firms led by CVC and Sainsbury's said that the news was 'not a deal-breaker', but added that it would prove difficult to resolve 'unless there is a lot more money put on the table'.
The paper also said that Bain Capital and Apollo Management had appointed investment bank Deutsche to advise on a possible rival bid for Sainsbury's.
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