The club announced at the weekend that the Ibrox legend is being treated for the illness.
Jardine, 63, made more than 500 appearances for Rangers 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, as it was for him, but outwardly he is handling it as well as you would expect.
"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.
"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: "Sandy has been an absolute tower of strength for me when the club was going through the administration period.
"It was well documented that we didn't have a board or a chief executive for a long time but Sandy was always around for a cup of tea and a blether.
"He is sadly missed around the place and we are all looking forward to the day he walks back through the doors of Murray Park and Ibrox."