The Halifax-born former England striker, now 67, had a playing career spanning 26 years and is regarded as one of the game’s mavericks.
Having started out with Huddersfield, Worthington went on to make over 200 appearances for Leicester, with spells at the likes of Leeds United and Sunderland following.
He made 32 appearances for Leeds in 1982, netting 14 goals.
Kim-Malou Worthington said: “There have been a few wondering about my dad’s health recently and so I thought I should let you all know Frank Worthington has Alzheimer’s.
“He was diagnosed several years ago and has been holding it off with positive thinking and football.
‘’They say several footballers from my dad’s era seem to have suffered the same disease, possibly due to the constant heading of the heavy football back in the day.’’
Another former England striker, Jeff Astle, died in 2002 from brain trauma which a coroner ruled was caused by heading heavy leather balls.
Alzheimer’s is the most common cause of dementia, symptoms of which include memory loss and difficulties with thinking, problem-solving or language.
Over the last 12 months, the families of England World Cup winners Martin Peters, Nobby Stiles and Ray Wilson have all spoken of the trio’s struggles with the disease.
Halifax-born Worthington, who played eight games and scored two goals for his country in 1974, was a flamboyant striker who, after leaving Leicester in 1977, took in a number of other clubs, ranging from Mjallby in Sweden to the Tampa Bay Rowdies in America.
Worthington also caught the eye with Bolton in 1979 when he scored a wonderful individual goal in a Division One match against Ipswich.
He was also a target for Liverpool in the early 1970s but a proposed move to Anfield collapsed because he failed his medical as a result of high blood pressure.
As Worthington’s career ran down he had shorter stints with lower league clubs in England, as well as Galway United in Ireland. He also managed Tranmere in the mid-1980s and was player-coach at hometown club Halifax in the 1991-92 season.
Worthington also released an autobiography entitled ‘One Hump or Two’ which contained entertaining accounts from his playing days, as well as stories about his life off the pitch in an era which included similar entertainers such as George Best, Stan Bowles, Rodney Marsh and Tony Currie.
Kim-Malou took to Facebook with the news and fans were quick to offer their support.
She said: “As time goes by there are moments when you see the effects of Alzheimer’s and this is hard sometimes for all those involved with a loved one who has this disease.
“It’s a funny thing that the one big lesson my dad always taught me was ‘mind over matter’...no matter how hard life gets, being positive will pull you through, every adversity is an opportunity for change and growth.
“Thanks dad, that is the biggest gift you ever gave me. And now this silly Alzheimer’s is taking you away from all that you taught me.
“My heart goes out to all those affected by Alzheimer’s, what a journey it is for all those affected.”