Thousands of shoppers now flood into the city centre every Sunday as most retail outlets open for at least afternoon trading hours.
The Herald has learned that the traders want to tap into this market and will formally ask the Dublin City Council to extend the terms of their on-street trading licence so that they can have the option of working seven days a week.
The traders, who sell fish, fruit, vegetables and other items, believe they have been missing out on a vital section of market
Cllr Christy Burke said: "This type of initiative should be welcomed, especially in a recession. They are trying to help themselves get over the downturn."
He added: "It will bring an uplift to the area and give Sunday shoppers an extra option."
A question has already been submitted to council officials in order to gauge their attitude towards the idea.
A meeting was also due to take place this morning between the traders and local representatives.
The Herald understands that shopkeepers in the area are supportive of the traders' move, as are business leaders.
The traders got the idea from their colleagues who trade on Henry Street throughout December to take advantage of the Christmas shoppers.
"If the Taoiseach announced 1,000 jobs there would be huge plaudits, but this is a positive thing too.
"It's a positive thing that a group of men and women are willing to work extra hard to keep their business up," said Cllr Burke. He added: "Why not let them give it a try and if it fails, it fails."
Dublin City Council is expected to issue the traders with a preliminary response next month, and if that is positive, Sunday trading could begin early in the New Year.
Moore Street in Dublin is one of the oldest surviving street trading districts in the city.
In the 1980s, Cllr Burke served time in Mountjoy Prison, along with the late Tony Gregory, in support of the traders.
Their existence was threatened again in a row over the price of a trading licence, but Cllr Burke says they are now looking to go bigger than ever.