On Thursday, the Ottawa Senators announced Melnyk needed an urgent liver transplant because his current health condition is "life threatening." The team put a public call out seeking a live liver donor.
There were 12 potential candidates being screened on Sunday, according to the team, and the transplant could take place this week.
Melnyk's rare AB blood type allows him to accept a liver donation from any blood type.
Melnyk had been quiet during this time as he was being treated for his liver condition. On Monday, though, the Senators' owner broke his silence in a written statement released on the team's website.
"The past few months have presented me with the greatest challenge of my life and up until most recently, it has been very personal and private," Melnyk wrote.
"Over the last few weeks, my declining health became considerably more critical and urgent. During this time, my family and a few very close friends have worked tirelessly to help save my life."
'Overwhelmed' by support from public
Melnyk, who turns 56 next week, explained no member of his friends or family were "medically suitable" as a donor and he had "exhausted" all options. His family then convinced him to reach out to the public, Melnyk wrote.
"Since the announcement of my situation became public last week, I have been overwhelmed by the outpouring of support from the public and the media. It is truly heartwarming to feel loved by so many people," he said.
"Words cannot even begin to express how thankful my family and I are for your expressions of support, your prayers, and your unconditional desire to help me in the biggest battle of my life."
Melnyk is currently at the Toronto General Hospital after he was admitted in late April. Doctors say his health remains stable and he is in great spirits, according to a statement from the Senators.
In his statement, Melnyk also wrote about raising awareness about organ donation
"I would encourage everyone to take a few moments to learn more about being a donor in their respective province or state. The act of helping one another is a powerful thing," he said.
"You have lifted my spirits, and in the process have given me all the strength I need at this difficult time. Thank you from the bottom of my heart."