Yasmin Nakhuda alleges the Japanese macaque, named Darwin, was illegally taken from her by animal control officials and moved to a sanctuary in Sunderland, Ontario, where he now lives.
Nakhuda is due in court Thursday to try to get an interim order to have returned to her.
Her lawyer, Ted Charney, says he has been told the sanctuary plans to ask for the case to be adjourned Thursday.
"Nakhuda has no claim of ownership over a wild animal that is no longer in her possession," the sanctuary said in its response to her filing to have Darwin returned.
A filing from the sanctuary asks for an adjournment on several counts, including a request that it be given more time to gather evidence.
The sanctuary also claims that it now owns Darwin, arguing that unlike domestic animals, wild animals are owned by the person that possesses them and Nakhuda voluntarily turned the monkey over to Toronto Animal Services.
The young monkey captured worldwide attention earlier this month when he was spotted wandering the store parking lot in a little coat.
Nakhuda, a real estate lawyer, said she was never given the chance to remedy the situation after being fined $240 for breaking the city's prohibited-animal bylaw.
"I've spoken to a number of people in the legal community and they do agree that there is no statute allowing the city to take an animal away based on the circumstances," Nakhuda said at the protest.
In court documents, Nakhuda says she, her husband and their two kids would be willing to move to a city that allows monkeys in order to keep Darwin, whom they consider part of the family.
Nakhuda said she hopes to have Darwin back by Christmas.
The primate sanctuary has said the monkey is doing well and the agency was prepared to fight any legal challenges for its return.