Deadline of November 8 given for Delta Two to make a formal offer
The Qatari firm first approached the supermarket giant in July but the credit market chaos caused by the US home loans market has heightened the Sainsbury family's concerns that there was too much debt in the offer.
But Delta has said that if a deal went ahead, Sainsbury's would see "significant investment and further expansion" and would remain "a robust competitor... even in challenging industry conditions."
Former Asda deputy chief executive Tony Campbell has been lined up to become a non-executive chairman if a deal is successful.