Last year the zoo announced it was going to relocate the pachyderms because after 40 years, the zoo couldn't give the animals the space they required.
A decision will be coming within six weeks after zoo officials finish visiting sites to determine the best placement for Kamala, Swarna and Maharani.
The zoo says the elephants' long-term welfare is better served by being part of a large social group; something that can only be achieved at a facility with more year-round space.
A decision on a new home for Spike, the male elephant, will be made in conjunction with the Miami Zoo, which still owns him.
Animal-rights organizations have taken issue with the decision of the Valley Zoo in Edmonton to keep its lone female elephant, Lucy.
They have pointed out elephants are by nature social animals and have said keeping Lucy alone at the Edmonton zoo in the winter months is like keeping humans in solitary confinement in Siberia.
The case has attracted the support of several celebrities, including retired game-show host Bob Barker and former hockey player Georges Laraque.
Zoo and city officials have said moving Lucy would be too stressful and could even be life-threatening for the elephant.
However, they have also said Lucy will be the last elephant to be housed at the Valley Zoo.
(CHQR, The Canadian Press)
Also on HuffPost