"The club is extremely disappointed in the sensationalised television news story on Monday night about this tragic situation.
"One of the most important factors for Alex at this time is hope, which was jeopardised by this report."
The 22-year-old was brought out of an induced coma after surgery on Tuesday of last week and has been conscious since.
He began communicating with his family on Sunday after his assisted ventilation was removed.
With McKinnon still in a serious but stable condition, visits have been restricted - meaning only coach Wayne Bennett and not his teammates were able to visit him.
The club said it planned to continue to provide factual updates in consultation with the player's family during this delicate time.
McKinnon's parents, Kate and Scott, as well as his partner, Teigan Power, thanked the public and media for their ongoing support and concern.
"While there is a lot of detail being reported about Alex's condition, it is important to remember that it is still early days for him post-injury," a family statement said. "Those close to Alex know he is strong and that he is a fighter, and that alone is reason to remain hopeful."
Melbourne Storm's Jordan McLean will face the judiciary tonight over the tackle.
- AAP
