The 49-year-old Mildura man is on trial in the South Australian Supreme Court charged with the murders of Mrs Harrison, 71, at Elizabeth South in 1998, Beverley Hanley, 64, at Elizabeth North in 2010 and Stephen Newton, 55, at Mt Gambier in 2011.
On Tuesday, Kryss Pumpa told the court he met Hainsworth in Mt Gambier Prison in 2011 and they became friends.
Asked if Hainsworth had spoken about Mrs Harrison's murder, Pumpa said: "He said he stabbed her and threw the knife in the bushes."
Mrs Harrison's body was found on the floor of the kitchen of her home by her daughter and grandson on March 3, 1998. She had multiple stab wounds to her chest and neck.
In 2007, a knife was found in a hedge at a property around the corner from Mrs Harrison's home.
Hainsworth, who lived next door to Mrs Harrison at the time of her murder, is also accused of murdering his aunt, Beverley Hanley.
Pumpa told the court that Hainsworth also spoke to him about "a relative he bashed with a blunt object", but he did not name the relative.
Defence counsel Andrew Fowler-Walker questioned Pumpa about his criminal record and asked if he was a fraudster, to which he replied: "Pretty much, but I'm not a granny killer".
He said Hainsworth had told him he was under a lot of pressure from the police.
Another witness, Lorrilea Crilly, said she had been a neighbour of Hainsworth's in Davoren Park in the late 1990s and had been in a sexual relationship with him.
"He stated that he bashed and stabbed an old lady at Elizabeth," she told the court.
Ms Crilly said she hadn't taken much notice of what he said because he was a "big talker" who "talked a lot of s***".
The judge-alone trial before Justice Adam Kimber continues.
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