The status would allow businesses to increase opening hours for 18 weeks of the year, and has already been awarded to several Northern Irish towns including Portrush and Newry.
BCC president Hugh Black said: “It [the status] gives the large stores the opportunity to open longer hours for 18 weeks from April until the end of September and we see that as an opportunity now with the number of foreign tourists.
“We're looking at it now and we’d like to talk to the city council about it with a view to having it in place next year.”
However, The Belfast Telegraph reported the lobby was likely to run into opposition from high-profile figures including High Sheriff of Belfast Jim Rodgers.
He said: “Sunday should be respected as a day for the family rather than for shopping. I’m a big supporter of the business community and I always have been, but I don’t think extending the current opening times is the answer. It won’t improve the city.”
He also cast doubt on whether extended Sunday trading hours would boost the economy, saying: “Trading hours have increased considerably in recent years and I’ve noticed that footfall on a Sunday has been declining.”
Plans to overhaul Sunday trading laws in England and Wales were recently dropped after being rejected by the House of Commons.