Clemence, who now works as England's goalkeeping coach, began to feel unwell on Friday when he missed training and he was absent for Saturday's 1-0 friendly win over world champions Spain.
"Ray Clemence has been unwell while with England and is having tests in hospital," an FA statement said.
Clemence, 63, was also missing when England trained on Monday ahead of Tuesday's friendly with Sweden.
"At this time Ray would like to thank everyone for the kind messages he's received and the FA would like to request privacy for his family," the statement added.
During his illustrious 23-year career, Clemence won three European Cups with Liverpool and also helped the Anfield club lift the old First Division title five times before moving to top-flight rivals Tottenham Hotspur.
Former England goalkeeper Ray Clemence hospitalised
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