McConkey's family raised $279,516 through crowd funding to pay for a new procedure available in Seattle that isn't covered by insurance.
His father said McConkey's bags were packed and he was ready to travel to start the treatment today, but he had not recovered from a bad infection.
"He has to be in relatively good health to be part of this study," his father Ross McConkey told The Early Edition's Rick Cluff.
McConkey is now at BC Children's Hospital on intravenous antibiotics and his father said the family is hoping he will be healthy enough to travel in a week.
"Time is not on our side anymore, we truly have to get him there as quickly as possible," he said.
Treatment experimental, potentially dangerous
The treatment McConkey hopes to receive is still in the study stages, and takes T-cells, a type of white blood cell, from the patient, re-engineers them, and puts them back into the patient's body using a method believed to attack leukemia more aggressively.
McConkey's father said the family was encouraged by the results the study has already seen.
"Where we had no hope at all a few of weeks ago, when we heard about this, we had at least something to offer our son," he said.
"We had a young man that had this treatment done in Seattle in our living room about 2 days ago. He's a year out of going down to Seattle and having the treatment. He's cancer free. He's in university."
There is no guarantee it works, and the potential dangers to the patient still aren't known.
McConkey was diagnosed with leukemia two years ago, and his body has already rejected two transplants. Doctors have given him just a few weeks to live.
His father said every treatment McConkey has received has come with big risks and his family feels this one is worth taking.
"As a parent, you never stop fighting for your child. Eventually his leukemia will take his life if we don't try everything that's out there."
McConkey said his son is fighting to get better from the infection, so he can continue his fight to get healthy.
To hear more of McConkey's story, click the audio labelled: Kyle McConkey's leukemia treatment on hold due to infection.