Details of the possible deal have not been released.
However, it would transfer ownership of the meters, and their profits, to New York-based investment firm Stonepeak Partners.
Council needs to approve the agreement
RELATED | Chicago parking meter deal: City's meters sold to another private company, Mayor Johnson says
On Wednesday, council is also taking up an effort to slow down planned raised for tipped workers.
The proposal would pause raises under the city's "one fair wage" ordinance.
It would freeze increases for two years at larger restaurants and delay them up to four years at smaller ones.
It comes just weeks after Mayor Brandon Johnson vetoed an attempt to completely block the wage hikes.
RELATED | Council fails to override Johnson veto of minimum wage increase freeze for tipped workers
Republican candidate for governor Darren Bailey spoke during public comment to apologize for calling Chicago a "hellhole" in the past.
IL GOP governor candidate Darren Bailey apologizes to Chicago
"To this city, I owe you something," he said. "I owe you an apology. I said somethings about Chicago that were wrong. What I meant was that the political class is failing us, I should have been more clearer, and I wasn't. So, I apologize."
Bailey went on to talk about why he's moved to Chicago and laid out his vision for Illinois.