Turner, 22, is serving a life sentence for strangling Ms Longley, his former girlfriend, in his parents' home in Bournemouth, southern England, in May 2011.
Turner's parents Leigh and Anita were jailed for 27 months in July last year for perverting the course of justice after they destroyed a confession letter from their son and took evidence from the murder scene.
They have recently been released from prison and returned home, the Southern Daily Echo reported.
Neighbours confirmed both Mr and Mrs Turner had been seen at the property in recent days, the newspaper reported.
During his trial, the court heard that Turner had "bullied, harassed, threatened and assaulted" Longley during their relationship, before going "absolutely nuts" in a jealous rage on the night he killed her.
Turner appealed to London's Court of Appeal to have his conviction quashed but that was dismissed in April.
Ms Longley, who moved to New Zealand when she was 9-years-old, had returned to the United Kingdom shortly before she was killed.
