The club announced at the weekend that the Ibrox legend is being treated for the illness.
Jardine, 63, made over 500 appearances for Rangers as a player between 1965 and 1982 and still works for the club.
McCoist told Rangers' website: "Sandy has been an enormous part of this club and the club has been an enormous part of Sandy's life for 40-odd years as well.
"It was obviously a shock to us all, a real shock. It was an even bigger shock for him, but outwardly he is handling it as well as you would expect him to handle it.
"He is a fine, fine man, a wonderful individual and he will be fine because he is a very fit man and has a tremendous spirit and desire to do well in whatever he does.
"I honestly believe that these things are a necessity when you go through a trauma in your life and Sandy will be, in my opinion, as well equipped as anybody to handle the situation.
"He will meet it head on. I know he is doing that and I spoke to his wife on a couple of occasions recently and while he is very unwell he has a tremendous spirit and is fighting."
McCoist also credited Jardine as having a major role to play during a turbulent period, which saw Rangers go into administration before being consigned to liquidation in the summer.
He added: "He's a tremendous source of help and a real education. He's been over the course before and has a wealth of experience of Scottish football and of Rangers.
"He's here for everybody at the club, and particularly in the tough period that we have had over the last six months or so.