The Lisbon Lion is currently battling dementia and receiving treatment in hospital.
But false rumours have been circulating on social media regarding the 79-year-old’s health.
And his family have been forced to set the record straight in a statement issued on the official Celtic website.
It says:“Further to speculation circulating on social media we would like to confirm the following. As is widely known, our father, Billy, has been battling dementia for some time.
“He is currently in hospital receiving treatment for an illness. However, at no time have the family been called to his bedside and reports of his death are untrue.
“Whilst we appreciate the love and appreciation shown towards our father, the current rumours are upsetting to us as a family.
“We would appreciate if people would refrain from spreading such stories and respect our request for privacy in this matter.”
The former Hoops captain enjoyed a glittering career at the Parkhead club, where he became the first Briton to lift the European Cup after a 2-1 win over Inter Milan in Lisbon in 1967.
McNeill also led Celtic to nine successive league titles and won seven Scottish Cups and six League Cups, before having two spells as manager.