JC Flowers - thought to be willing to pay around £4bn for the business - wrote to Friends' board looking to open discussions last week, according to a report.
But the call is said to have been rejected by the insurer's advisers on Friday as JC Flowers put forward no firm proposals or detailed financial terms.
The New York-based private equity firm - which looked at a possible rescue deal for crisis-hit mortgage lender Northern Rock last year - has built up a 2.7 per cent stake in Friends Provident.
Despite indications of a 175p a share approach from Flowers, the insurer is holding out for 200p - valuing the company at more than £4.6bn - the report says.
The latest manoeuvring from Flowers comes weeks after Friends unveiled the results of a strategic review following the collapse of its £8.6bn merger with closed-life insurer Resolution last year.
Friends is cutting around 600 jobs as part of a sweeping overhaul and said a £440m hit would almost wipe out last year's profits.
The warning has seen the firm's share's plummet nearly 20 per cent since the end of January.
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