The organising committee and chief executive of Culture and Sport Glasgow Bridget McConnell have agreed to meet with former Socialist MSP Carolyn Leckie, who launched a petition opposing the plans to demolish five of the six tower blocks.
She will be joined by Len Bunton, the son of the architect who designed the high-rise flats, who has also spoken out against Glasgow 2014's decision.
Sam Bunton designed the blocks, which were originally built to help tackle the post-war housing crisis in the city.
It came as the petition gathered more than 12,000 signatures. The meeting will take place next Tuesday morning at the Commonwealth Games offices in Albion Street.
A Glasgow 2014 spokesman said they welcomed the opportunity to discuss the plans and they would "share more about the context and importance of Red Road's role within the ceremony".
Ms Leckie said she would approach the meeting "positively" and said it was encouraging that the committee was "showing signs of listening".
She said the massive number of signatures on the petition shows "that our instinct was ultimately right".
She added: "It becomes more polarising by the day. I don't think the Games Committee can keep thinking this will blow over. It will be embarrassing if at least half of the stadium are unhappy about it on the day of the opening ceremony and are jeering instead of cheering.
"I think it would be good if they responded to people's views and lived up to what they say about involving the community."
Meanwhile, people are continuing to have their say on the controversial plans.
Philip McCulloch, director of 1st Architects and a former Red Road resident, said the Games should not be a "basis for demolition".
He added: "I am amazed that the council are prepared to allow, on international television, the screening of the demolition of these flats.
"How frustrating it must be for the rest of the world to see the potential for housing being demolished."
The story has also created a buzz on the Evening Times website. Catherine McLachlan, from the city centre, said: "Please do not ruin the games in Glasgow, what on earth are you thinking of? We are all proud of our city."
Pete Gibson, from Lanark, said:"No matter which way they spin it, it's still and gross embarrassment having the opening ceremony featuring this. Glasgow City Council, get your act together before it's too late."