Social Development Minister Margaret Ritchie has announced a review of Northern Ireland's gambling laws.
Ms Ritchie said the current legislation dating back to 1985 was "not robust enough to deal with modern gambling".
In 2006, the British government brought in plans for new laws in NI - including allowing Sunday opening for bookmakers and bingo halls.
However, the changes, planned for 2008, were never introduced after the return of devolution.
Ms Ritchie said: "Current legislation is old, inflexible and hard to understand and the gambling market has moved on.
"There are new products and new ways of gambling that the current law never envisaged.
"It is in everyone's interests that the gambling industry is regulated effectively which is why I am initiating this review."
Bookmaker Adrian Eastwood said the current laws were antiquated and he hoped news laws would allow NI bookmakers to open on Sundays.
"Many people in Northern Ireland do bet on Sunday if they've got access to telephone accounts or the internet," he said.
"But the ordinary man in the street with a few pounds in his pocket likes to go to his betting shop but he can't do that, he's denied his right to do that.
"So what he does is he goes to his local pub or club where people are catering for him illegally."
Gareth Wallace of the Salvation Army said it did not think betting shops should be allowed to open on Sundays in NI.
"I don't believe the people of Northern Ireland want to gamble on a Sunday," he said.
"In Britain the only day of the year that people can't gamble is Christmas Day.
"Are we really saying we want to gamble on Good Friday in Northern Ireland, do people in betting shops want to have to work on Sundays?"