Gavin McGuire, 55, repeatedly told the High Court in Edinburgh he had never been in Elaine Doyle's home town of Greenock in his life.
The court heard how detectives questioned him about unsolved killings after he was convicted of murdering teenager Mhairi Julyan.
In the dock is John Docherty, 49, who denies strangling Ms Doyle near her home in Ardgowan Street, Greenock, on June 2, 1986.
As part of his defence, the jury have been given a list of 41 "possible suspects" which, it is claimed, may include the real culprit.
Defence QC Donald Findlay said he was not directly accusing McGuire of Ms Doyle's murder but, of all the 41 names listed, he best fitted the profile. "What I will suggest is that, undoubtedly, you could have been the killer of Elaine Doyle," he said.
McGuire replied: "I know that is what everybody is saying."
McGuire, whose first conviction for a sex attack dated from the 70s, said he murdered Ms Julyan "in a moment of madness" but he told the jury over and over again: "I did not kill Elaine Doyle."
The trial continues.