Delta Two is understood to have been given the green light from Qatar to increase the cash component of its £10.6 billion bid for J Sainsbury as it seeks the board’s backing to open the group’s books later this week.

Sources said that Delta Two, which is funded by the Qatari royal family, planned to give in to the board’s demands by offering up to £500 million in additional cash.

It hopes the revised proposal could lead to the group’s books being opened for due diligence as soon as the middle of this week, after nearly three months of negotiations.

But Delta Two’s long-sought deal to acquire Britain’s third-largest supermarket chain is still far from settled, given that the bidders have yet to hold any talks with Sainsbury’s pension trustees or to gain the approval of its founding family shareholders.

The board, led by Sir Philip Hampton, the chairman, and Justin King, the chief executive, has argued that the level of debt included in the Qatari bid could make it more difficult for Sainsbury’s to compete in the event of a downturn in consumer spending.

Delta Two, however, believes the capital structure of its 600p-a-share bid is sound and has so far resisted calls for more cash. But in recent weeks it has decided that it has to capitulate in an attempt to move the process forward, although it is understood that the final cash injection could be less than the mooted £500 million.

Sir Philip also faces pressure from the Sainsbury family, who control about 18 per cent of the group and blocked an earlier bid from CVC Capital on the grounds that it undervalued the company and was too highly leveraged.

However, one source said last night that if the board signed off on the capital structure it would be difficult for the family to go against it.

A heavily indebted bid is also more likely to incur the wrath of the pensions trustees and encourage them to demand a higher upfront payment from the Qataris.

Sainsbury’s board faces a tough decision. It cannot argue with Delta Two on price, because it had already agreed in principle to back CVC’s 582p-a-share bid. But it does not want a repeat of the CVC situation, which ultimately failed because the family refused to back it.

Delta Two owns a 25 per cent stake in Sainsbury’s and is its largest shareholder.

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