The deal sets aside 10 percent of all hours worked for minority apprentices.
Jones believes that minority workers, especially those living on Chicago's South and West Sides, deserve 40 percent of all work hours.
"I'm talking about people working on the job actually out there doing the work. The building trades in Cook County have historically discriminated against minorities," Jones said.
Chicago Mayor Richard Daley denied Jones' assertion.
"We're very proud of the participation we have with people in that community. It's not a sham," Daley said.
Jones is calling on both sides to go back to the drawing board and work out a new deal.