According to reports, a prisoner tried to spit at the 84-year-old but missed and hit a man sitting next to him.
The prisoner next to him then retaliated, sparking a fight between several inmates.
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A source told a UK newspaper: "There was one prisoner who looks like he wanted to make a name for himself and tried to spit at him. "It didn't hit, but it got close.
"Then all of a sudden another guy came steaming in and a fight started."
ROLF HARRIS SENTENCED TO FIVE YEARS AND NINE MONTHS IN PRISON
"You could see Rolf was shocked by what happened,” the source added.
Harris was convicted of indecent assaults on girls as young as seven-years-old.
KATIE PRICE SAYS ROLF HARRIS SHOULD 'SUFFER'
He was jailed for five years and nine months and is currently serving at HMP Bullingdon in Oxfordshire.
Though Harris was not directly involved in any physical fighting during the altercation, the source revealed that he has become a ‘hate figure’ in the prison due to the nature of his crimes.
The incident comes following news that Harris is reportedly planning to appeal against his convictions.