The zoo has been negotiating with representatives of CUPE Local 1600 for several months, but no agreement has been reached for more than 400 permanent, part-time and seasonal workers.
The workers include zookeepers, educational staff and veterinary technicians.
The union says it made "a comprehensive offer" to the zoo.
Christine McKenzie, the president of CUPE Local 1600, says the union "absolutely has no intention of striking" and believes that a deal can be reached.
But McKenzie also said that the union has learned that management has been taking steps to ensure they are ready for a lockout.
"I'm sure that they have a plan in place for taking care of the animals, but it's going to very difficult for them if they put themselves in that situation," she told reporters.
McKenzie said the zoo requested a no board report earlier this month, which set in motion "a countdown to a work stoppage."
The zoo is just days away from expanding its hours for the summer and is due to open its much-anticipated panda exhibit soon.
Two giant pandas arrived in Toronto last month, to begin a 10-year stay in Canada.
Er Shun and Da Mao will spend the first five years of their visit to Canada in Toronto. They are due to spend the rest of their time in Calgary.
McKenzie said that the "two key people" that have been taking care of the pandas are among the workers who could be locked out.
The Toronto Zoo has not hosted pandas in almost three decades. The last time was in 1985.
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