"This is going to be done from the ground up," he told the paper, adding that he plans to announce his bid Sunday with community leaders on the steps of City Hall.
"I think the speaker should be a facilitator, not a dictator," Barron said. The former Black Panther admitted that "it's a long shot" that he'll win.
The council votes on the position in January, and Quinn may have some trouble, as many of her colleagues -- and constituents -- were upset about her siding with Mayor Bloomberg on the term limits issue.
Barron said he plans to team up with Councilman Tony Avella to suggest changes for the speaker position.
On Tuesday, Barron made headlines when he argued with City University Trustee Jeff Wiesenfeld during a groundbreaking ceremony for a new building at BMCC.
Quinn also made news this past week when she teared up at a press conference discussing the failure of the gay marriage vote in Albany.