West Ham argued their own research into the real cost of relegation, when all the savings from wages and recruitment had been taken into account, was no greater than £5m.
It appears a final settlement in the region of £10m has been agreed upon, which represents a victory for Sheffield United - but on terms acceptable to West Ham.
Sheffield United's claim for damages was supported last year by an independent FA tribunal chaired by Lord Griffiths.
West Ham are close to finalising a compensation agreement with Sheffield United worth around £10 million to end the long-running Carlos Tevez saga.