The Independent on Sunday said the two bidders were the most disappointed by the decision. Once the undertakings are agreed, Morrisons will be free to resume its bid - perhaps by early next month.
The Co-op, Waitrose, Marks and Spencer and DIY retailer B&Q have all emerged as candidates for the 53 Safeway stores that are up for grabs following the Competition Commission ruling.
The Business said the retailers were among a number of bidders to have submitted offers for the stores, which could fetch up to £500m.
Asda has made big gains in childrens clothing over the last six months, according to Taylor Nelson Sofres figures obtained by the Financial Mail on Sunday.
The paper said Asda’s share was 21%, behind market leader Next with 32% and second-placed Matalan on 29%.
The losers in volume terms were Marks and Spencer down 10%, and Woolworths with a fall of 7%.
Homeware ranges at Sainsbury, Tesco and Marks and Spencer have impacted on the growth of Swedish group Ikea, according to new figures from retail analyst Verdict, the Sunday Times reported.