Results of the vote are expected late Tuesday night.
The 23,000 inside workers include child care workers, ambulance dispatchers, nurses, janitors and parks and recreation staff.
Workers can strike or be legally locked out on Saturday, which means daycares, most recreation centres and city-run swimming pools would be closed.
But CUPE Local 79 president Tim Maguire says the union has no intention of walking off the job Saturday, even with a strike mandate.
Maguire says union negotiators want to stay at the bargaining table and carry on talks if the city is willing.
"Local 79 has no intention of walking off the job this Saturday morning simply because we don't have a collective agreement," Maguire told a news conference.
The union has accused the city of bargaining in bad faith and filed a complaint with the Ontario Labour Relations Board.
But the city says the union has been unavailable for negotiating for seven of the last 17 days.
(680News, The Canadian Press)