A source close to the company said Sir Ken Morrison had signed a revised draft of undertakings from the Office of Fair Trading, although he could still wait for three weeks before revealing his hand.
After receiving the legally binding undertakings from Morrisons, the OFT will then pass them to the DTI for approval and publication.
Once they are published, Morrisons can make a fresh bid.
But this needs to be done within 21 days, or Morrisons must receive a recommendation from the Safeway board of directors in order for the takeover to go ahead.
On September 26, trade and industry secretary Patricia Hewitt asked the OFT to negotiate undertakings with Morrisons relating to store divestments.
She also asked it to obtain undertakings from Asda, Tesco and Sainsbury that they would not acquire any part of Safeway other than a handful of the 53 stores Morrisons had to divest.
Hewitt later relaxed some of the restrictions on the unsuccessful bidders and suggested they could buy other parts of Safeway if cleared by the OFT.