Big supermarkets and other major retailers have been in talks with the Government about relaxing Sunday trading laws after longer opening hours were allowed during the Olympics.
Retailers, trade bodies and the Government are thought to be discussing the impact of the temporary lifting of restrictions, with a view to a permanent change.
Asda is among the firms providing customer feedback on the extended trading hours for the Games, according to the Mail on Sunday newspaper.
The Walmart-owned firm is understood to be in favour of allowing permanent longer opening on Sundays after what it claims was a successful relaxation earlier this month.
Retailers are only allowed to trade for six hours on a Sunday, between 10am and 6pm. But the Government passed emergency legislation to relax the law during the Olympics and the upcoming Paralympics.
Andy Clarke, chief executive of Asda, reportedly said: "The extended hours have become more popular as time has moved on."
Communities Secretary Eric Pickles is believed to be open to the possibility of a permanent change.
The restrictions are designed to protect smaller, family-run stores from competition from supermarkets, by allowing shops of less than 3,000 sq ft to open for longer than six hours.
Many supermarket-owned convenience stores already qualify under these rules as small shops.