The Ibrox club confirm that the former Scotland international is suffering from the illness, pledging that they will fully support the 63-year-old and his family
The former defender made over 500 appearances for the Gers between 1965 and 1982 and earned 28 caps for Scotland, scoring one international goal.
In a statement on their official website, Rangers declared: "The club will support Sandy and his family in any way it can throughout his treatment and we ask that the media respect his privacy and indeed the privacy of his family."
Jardine, who also won the European Cup Winners' Cup in 1972 with the Glasgow club, is held in high regard by everyone connected at Ibrox.
"Sandy is a true Rangers legend in every sense of the word and has the admiration and respect of every one of his colleagues at Ibrox and Murray Park," the club stated.
The former centre-back also made over 200 appearances for Hearts, whom he later went on to manage between 1986 and 1988.