The country's highest court must decide whether to reinstate Grant's murder conviction or side with the Manitoba Court of Appeal, which ordered a new trial for him in 2013.
The provincial appeal court said the original trial judge did not consider some evidence that could have cast doubt on Grant's guilt.
Manitoba prosecutors appealed the decision to the Supreme Court, which heard arguments in November and will issue its ruling on Thursday morning.
Derksen's mother Wilma said her family is ready for whatever the court decides.
"The part of this waiting ... isn't so much what the decision is going to be but we know that it's going to create a change — something's gonna change in our lives and in some ways that's the reluctance. We don't know what that change is gonna be," she said.
"I think at this point it isn't so much about Candace anymore, and I think that's how we have been able to live with it. This now becomes an important decision about everyone else — in the justice system, in the community."
Derksen was 13 years old when she disappeared on her way home from school on Nov. 30, 1984.
Her body was found six weeks later, bound and frozen, in a storage shed not far from her family's home in Winnipeg's East Kildonan neighbourhood.
Grant was not charged until 2007, after numerous tests on a piece of twine used to bind the teen.
A jury found him guilty of second-degree murder in February 2011, and he was sentenced to life in prison with no parole eligibility for at least 25 years.
Grant has repeatedly denied killing Derksen.
If the Supreme Court of Canada sides with the Court of Appeal, prosecutors must decide whether to proceed with a new trial or drop the case.Suggest a correction