Jardine, 63, who was capped 38 times for his country and still works for Rangers in a public relations capacity, is receiving treatment for liver cancer.
Football clubs, players and fans have taken to social networking sites to wish him well.
Celtic FC posted on Twitter: "Everyone at Celtic is very saddened to hear that Sandy Jardine has cancer. Best wishes to Sandy and his family at this time."
Former Rangers midfielder Maurice Edu said the diagnosis was "terrible news" and wished the former defender a speedy recovery.
Stoke City and Scotland player Charlie Adam, once of Ibrox, added: "Shocked to hear news about Sandy Jardine. Hope he recovers from it. True Rangers legend."
Stenhousemuir FC added: "Everyone at Stenhousemuir FC would like to pass on our best wishes to Sandy Jardine and his family in his battle against cancer. Be strong!"
The news was revealed on the Rangers website on Saturday. In a statement, Jardine said: "I would like to thank everyone for their best wishes. As you can appreciate this is a difficult time for me and my family and I ask that you respect our privacy."
A Rangers spokesman added: "There is little doubt Sandy will fight this disease in the same way he fought bravely in every match."