Tracey Browne was just 14 when she was bludgeoned on the head five times by a man wielding a hammer in 1975.
Browne, now 56, believes she survived the attack because her assailant - long suspected to be Sutcliffe - was disturbed by a passing car.
Now The Sun on Sunday claims to have Sutcliffe on audio tape confessing to the attack, which left Browne unconscious and bloodied with serious head injuries.
Sutcliffe, who now calls himself Peter Coonan, is alleged to have said: “I saw this Tracy Browne. She didn’t look 15 [sic – she was 14] – she looked about 19 or 20. She were all dressed up. She were walking slowly up this lane.”
Claiming he mistook her for a prostitute, he added: “Anyway, I hit her with a branch or something, didn’t really injure her, and threw her over a wall.
“And I climbed over the wall and I was thinking of bumping her off and this voice said, ‘Stop, stop. It’s a mistake.’”
Two months later Sutcliffe killed his first victim Wilma McCann.
In response, Browne told the newspaper: “My injuries weren’t caused by a blow with a stick. I was hit with a hammer five times, for God’s sake. I’ve got the dents in my skull to prove it.”
A spokesman for West Yorkshire Police said the force had not been approached by the tabloid about the alleged recording and currently had no comment on the matter.
It comes just months after news that Sutcliffe was reportedly questioned in jail over 17 unsolved attacks, including Browne’s.
Sutcliffe murdered 13 women and attempted to kill seven more between 1976 and 1981.
In August it was reported the 70-year-old had been moved out of Broadmoor psychiatric hospital and into HMP Frankland in Durham.
The former lorry driver from Bradford had spent 32 years inside the high-security institution in Berkshire after he was diagnosed with paranoid schizophrenia following his life sentence in 1981.
He will continue to have his mental health assessed in prison and could be returned to a psychiatric hospital if there is a change in his condition.
Most of his victims were prostitutes who were mutilated and beaten to death.
He was given 20 life terms for the murders and was caught when police found him with a prostitute in his car.
They became suspicious and found he had a fake licence plate and weapons including a screwdriver and hammer in the boot.
Before he was moved to Broadmoor, the killer spent three years at Parkhurst prison on the Isle of Wight.