The speedy Carlisle born winger was signed by manager Bill Shankly from Preston North End, where he made 121 appearances.
He scored 54 goals in 416 appearances for Liverpool before going on to end his career at Bolton Wanderers where he helped them to the second division title in 1978.
His former team mate Ian Callaghan told the Liverpool Echo that Thompson had been a key part of the successful era created by Shankly.
“It's such sad news. Peter was such a fantastic player and a big part of the club's success in that era.
“He had a real gift for dribbling with the ball and holding on to it. Peter was a really special player, he really was."
Thompson won 16 caps for England.
(Reporting by Simon Evans, editing by Pritha Sarkar)
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