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His family confirms this in a statement, according to the BBC, Sky Sports and The Guardian.
– We are sad to announce that Joe passed away peacefully this afternoon surrounded by his family, they write.
He lived to be 77 years old.
Kinnear earned 26 caps for Ireland during his career. He won the FA Cup, the League Cup twice and the UEFA Cup with Tottenham as a player.
He was manager of Wimbledon, Luton, Newcastle and Doncaster Rovers, as well as national team manager for India and Nepal.
He led Wimbledon to 6th place in the Premier League in the 1993/94 season. Kinnear suffered a heart attack in 1999 and passed out at Wimbledon shortly after, according to media reports.