Kokkinakis was born in Adelaide to Greek immigrant parents, Trevor (Tryfon) from Kalamata, Greece and Voula (Paraskevi) from Tripoli, Greece.
In August 2015, Kokkinakis was thrown into the centre of a scandal sparked by compatriot Nick Kyrgios, who suggested during a match against Stan Wawrinka at the Montreal Masters that Kokkinakis had had an affair with Wawrinka's girlfriend, Croatian tennis player Donna Vekić [REF].