Authorities released few other details ahead of the news conference, which was set for 1pm (2100 GMT), and did not say whether or not the suspect was alive to be arrested or charged in the 40-year-old cold case.
Karen Klaas, 32, was attacked at her home in the Los Angeles suburb of Hermosa Beach on the morning of Jan 30, 1976. The mother of two had been sexually assaulted, strangled and left in a coma, dying at a local hospital five days later.
The case has remained unsolved for four decades despite working up a DNA profile of the killer based on forensic evidence found at the crime scene.
Familial DNA testing involves using a national DNA database to search for people who may be related to the suspect.
Klaas and Medley, who with Bobby Hatfield made up the singing duo best known for such hits as “You’ve Lost that Lovin’ Feelin'” and “Unchained Melody”, were married from 1964 to 1970.