Emanuel wants to change the name of the major route from 56th to 130th streets to “Reverend Bishop Brazier Avenue” and is expected to propose the idea to the City Council Wednesday.
Brazier marched with the Rev. Martin Luther King Jr. when he came to Chicago in 1966.
The minister, who died in 2010 at age 89, spent nearly 50 years as a pastor of the Apostolic Church of God in Woodlawn and became a bishop in 1976.
He helped create the influential Woodlawn Organization, which in the 1960s successfully fought the University of Chicago's South Side expansion that threatened to displace black residents.
His son, Byron Brazier, who took over as the leader of his father's church in 2008, said it would be "a huge honor" if the street is renamed.
"We're just thrilled at the prospects of it," Byron Brazier said of he and his congregation. "It certainly lends itself to the legacy my father had ... and all the work he has done for the people in Chicago."
The pastor said he told his congregation two weeks ago that the renaming was "something that could happen."
"Everyone stood up and cheered and clapped," he said.
Byron Brazier credited his father for growing the church to about 20,000 members while also working as a community builder by focusing on education and affordable housing.
“Bishop Brazier was a spiritual and community leader on Chicago’s South Side, fighting against crime and poverty, while advocating for better housing and schools,” Emanuel said in a news release.
“By renaming Stony Island Avenue in his memory, we are honoring a man who influenced generations of pastors and parishioners to spiritual worship with community activism,” the mayor said.
While streets often are renamed honorarily with a separate brown sign next to the city's street sign, this renaming would change the city's official sign, the Mayor's Office said.
It would be the first time the city has officially renamed a major road since King Drive was given its new name after the Rev. Martin Luther King Jr., city spokesman Bill McCaffrey said. Once Grand Boulevard and later South Park Way, it became Dr. Martin Luther King Jr. Drive in 1968.
According to "Streetwise Chicago" by Don Hayner and Tom McNamee, Stony Island got its name from a limestone ridge that once protruded from the lake. The ridge ran alongside Stony Island between 92nd and 93rd streets.