Dublin City Council has said it will consider moving the Molly Malone statue if the installation of flowerbeds around it does not deter people from touching the bronze sculpture's breasts.
Flowerbeds are to be installed around the statue in Dublin city centre in the coming weeks.
The tradition of rubbing the famous fishmonger's breasts for luck is believed to have begun around 2012 and is thought to have been instigated by an imaginative tour guide.
However, it has resulted in the statue becoming discoloured around the figure's neckline.
Dublin City Council Arts Officer Ray Yeats said that the measure had helped reduce anti-social behaviour at Dublin's Portal installation, but that if it did not work, the council would have to consider other options.
"Using planters around precious objects is a strategy that seems to work. It worked well with the Portal. If it doesn't work, we'll be back to the drawing board, but everything is on the table. We're considering everything from raising the plinth to moving the statue. We'll do what we have to do," Mr Yeats said.
Mr Yeats said the practice was difficult to combat as it happens to statues worldwide.
"We don't want people to touch any statue anywhere in the city. I think that it's a question that affects statues throughout the world.
"I think the idea gets around that you touch the statue for luck or something, so this happens to statues in various countries, not just to women, but to male statues and to animal statues as well," he said.
The majority of people at the statue supported the move to discourage touching Molly Malone's breasts.
John Parkhill, a tour director with EF tours, is currently bringing a group from North Carolina in the US around Ireland and had asked them not to grope the statue.
"It sends the wrong message about women and it doesn't do the material that the statue is made from any good.
"Our whole ethos is responsible travel. In the far east where we tour we don't ride elephants, when we're in America we don't swim with the dolphins, and we discourage them from touching Molly Malone," Mr Parkhill said.
A group of young people from Sheffield in the UK said they also supported the move.
"If you wouldn't do it to a live woman, I don't see why you would do it to a statue. It just sends a really kind of derogatory message, in my opinion," one woman said.
Her male companion agreed and said "I think it's a bit strange, especially when I've just seen, like, literally, a tiny kid doing it. It feels a bit odd".
However, another Spanish woman, who used to live in Dublin, said she did not see a problem with the practice.
"I believe in good luck. I don't believe in bad luck. So it's okay, if they think that will bring good luck, it's okay," she said.
In May, Dublin City Council hired stewards to patrol the statue to discourage the behaviour but they said the week-long pilot showed that monitoring of the statue was unsustainable.
Ray Yeates said that while people did respond to requests from stewards not to touch the statue, when it was not being patrolled, the touching quickly resumed.
Mr Yeates said it appears the practice of rubbing the breast area of Molly Malone has now become "ingrained" and that having the statue patrolled daily "is not a sustainable solution".
Mr Yeates also said the council had explored the option of raising the height of the statue but that could cost in excess of €100,000.
He said a number of departments in Dublin City Council will have to be consulted about the new plans to protect the statue but that he hopes to have approval for the flowerbed solution in the coming weeks.
Mr Yeates said: "I don't want people to touch the statue at all. Where people are touching it, it is disturbing for some people, for others it's not, but the damage to the statue is the main reason we don't want this to go on."
