The serial killer, 73, supposedly believes an interview with Morgan will get him out of prison.
Sutcliffe made the suggestion after watching Psychopath, in which Morgan grilled killers Paris Bennett over the murder of his younger sister, The Sun on Sunday reports.
He reportedly told a pal at Falkland Prison: “I saw that Piers Morgan show and it was really interesting – they did it from all sides.
“I wish someone like him would look at my case because it’s never been done from my point of view.
“I wish someone like him would look at my case because it’s never been done from my point of view”
“If they did it properly they would examine all the faults with my trial and how the judge overruled all the doctors, which was wrong.
“People don’t realise it was a mental illness but I went on full trial.”
Sutcliffe was convicted in 1981 of murdering 13 women and attempting to kill seven more.
He was sent to the facility in Berkshire in 1984 after being diagnosed with paranoid schizophrenia.
However, a health tribunal ruled that he no longer needs treatment for the mental disorder.
Sutcliffe, from Bradford, preyed on women in West Yorkshire and Manchester from 1975 to 1980.
The beast, who worked as a lorry driver during his reign of terror, usually beat them to death with a hammer before mutilating their bodies.
During his trial, Sutcliffe claimed that God had ordered him to murder his victims.
The former gravedigger said the voice came to him from the headstone of a Polish man in a cemetery where he worked.