The 74-year-old had an illustrious playing career which included spells at Liverpool, Hamburg, Southampton and Newcastle United, while he twice won the European Footballer of the Year award.
Keegan moved into management after ending his playing career and had stints in charge of Newcastle United, Fulham, England and Manchester City.
"Kevin was recently admitted to hospital for further evaluation of ongoing abdominal symptoms," his family said in a statement.
"These investigations have revealed a diagnosis of cancer, for which Kevin will undergo treatment. Kevin is grateful to the medical team for their intervention and ongoing care. During this difficult time, the family are requesting privacy, and will be making no further comment."