The park district said earlier if an agreement couldn't be reached about 100 layoffs would be part of the Chicago Park District budget.
Those who would take the furlough days include park supervisors, lifeguards, physical instructors, cultural instructors, building attendants, and many other union workers.
The agreement must be ratified by rank-and-file workers.
The board will vote on the 2010 budget Wednesday at 4 p.m.