McDonald has been battling a chronic kidney disease since the age of 18 and is due to have surgery next month.
The 32-year-old hopes to play again after his scheduled transplant, with friends and family having put themselves forward to become donors.
McDonald was left out of the Cottagers’ two 25-man Premier League squads this season and was expected to leave the west London club on loan during January.
After going public with his news, McDonald will now focus on recovery, which Parker believes he will tackle with as much vigour as he did games on the pitch.
“He has been as good as gold, really. I spoke to Kev a few weeks ago regarding his situation,” Parker said ahead of Thursday night’s Premier League match against Tottenham.
“People at the club and myself have been aware of it, that there has been an issue for Kev for some time.
“In terms of when it would be needed for him to have that operation, it has come at this point.”
Parker added: “He has got a big few months ahead of him. No doubt the way he is as a fella and what he is about, he will come out of this and hopefully be as good as ever.
“In terms of his decisions at the end of it, I still think he is not sure what he wants to do.
“But the main focus for Kev and everyone else is that he gets better after the operation and then decides what is best for him from there.”