The 64-year-old Irishman, a mainstay of Stoke's 1970s side and scorer in the 1972 League Cup final victory over Chelsea, was in intensive care at the University Hospital of North Staffordshire after a suspected vascular aneurysm.
Stoke said on their website that Conroy, who had surgery yesterday, was in a critical but stable condition.
Legend: Terry Conroy (right) and Jimmy Greenhoff celebrate reaching the 1972 League Cup Final
'Our thoughts are with Terry and his family at this time and we are all praying and hoping for the best in his recovery,' chief executive Tony Scholes told stokecityfc.com.
'Terry is Mr Stoke City through and through, as well as being a player of legendary status at this club during the most successful period in our history.'
Conroy has continued his association with the Potters, working as a match-day host, and was at the Britannia Stadium for Saturday's 4-0 win over Newcastle.
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