It's the former site of the Michael Reese Hospital, which has been closed for 16 years.
The 48-acre site in Bronzeville is still ripe for development.
"This could be a great opportunity as we work side by side with the community, and I believe we can do this and create something we can all be proud of," 4th Ward Alderman Lamont Robinson said.
In the past, the Bears have rejected the site, saying it was too narrow and presented engineering and security challenges because of Metra tracks on the property.
In April, the Bears released plans for a new state-of-the art stadium on the lakefront next to Soldier Field, their current home.
They offered up more than $2 billion of their own money to build it, but said they also needed at least that much in public funding.
And that plan has gone nowhere among lawmakers in Springfield.
"I think they are just recognizing there's not a lot of political will behind them for the south lot," said Danny Ecker, with Crain's Chicago.
While the Bears stadium focus has apparently shifted again, they still own the $197 million 326-acre site in Arlington Heights.
And the mayor of Arlington Heights said the town remains in talks with the team about building on the former home of the Arlington Park race track.
Some observers believe the Bears still may wind up going the suburbs.
"Arlington Heights still makes the most sense. I say that unequivocally," said Marc Ganis, with SportsCorp. Ltd.
Ganis has been involved in dozens of stadium deals around the world. And he said, if the Bears are determined to stay in the city, the South Side appears to be the leading option at this point.
"We need to get this site developed, and the community deserves that," Robinson said.
Bears spokeswoman Tarrah Cooper had no comment on the reports the team is in talks regarding the Michael Reese site.