Hill, now 85 and retired from broadcasting, contracted Alzheimer's five years ago, though his family only made his illness public at the weekend.
It has emerged that several of his children are embroiled in a legal battle with his third wife, Bryony, over a power of attorney agreement which he signed back in 2005 to give Bryony and a lawyer joint power to control his affairs.
Hill is most famous today for his time as a presenter and pundit on the BBC's Match of the Day programme - not to mention his prominent chin. But he also enjoyed a distinguished playing career with Fulham and Brentford, and was the manager who took Coventry City into the First Division for the first time in the club's history.
He also became chairman of the PFA, and is widely acknowledged as the man who ended the wages cap for footballers which limited their earnings to just £20 a week - a rule which had previously meant many of the greatest stars of earlier generations ended their days in poverty.
Hill's hugely successful career on and off the pitch - which included 25 years as a mainstay of Match of the Day, from 1973 to 1998 - means that he has no financial worries, but his very affluence appears to have been the cause of tension.
His son Jamie, who was born to Hill's second wife Heather, told the Telegraph he was not happy that his father's third wife and the lawyer had the power to make all the decisions - and even more unhappy that they have refused to give up any of that power.
"Because of the power of attorney, the children have no say over decisions over dad’s health care or his assets," he said.
"He is the most sprightly physical specimen in the home, but his mind is not what it was. The home is the best place for him. That is not my complaint.
"My concern is we only discovered in 2008 that power of attorney was signed three years earlier. We said in 2008 if Bryony’s lawyer steps aside and one of us children has joint power of attorney, we will be happy. Unfortunately, that was declined."
62-year-old Bryony has refused to comment, though Jamie was adamant that all he wanted was the right to have a say: "I don’t want to make this personal. It affects many other families, and I want to highlight it.
"This will become a more common problem over the years because there are so many families in the same position as ours."
Jamie's sister Joanna echoed the same concerns.
"It is a shame that we as his children have no rights over his treatment and care. Children whose parents have married more than once should be made aware that they will be unable to influence their affairs if they register a power of attorney," she said.
"Children should talk to their parents, before deterioration sets in, about how they want to be looked after and whom they want to be in charge of their lives."