Wuxuu bilaabay 2013 isagoo buuxinaya kooxaha Mareykanka iyo Jarmalka inta lagu gudajiray Koobka Hopman ee 2013
asigoo badalaya dhaawaca John Isner iyo Tommy Haas. Kokkinakis ayaa ku tartamay tartankii isreebreebka ee tartanka Australian Open ee 2013, waxaana laga badiyay Steve Johnson 15<unk>17 setkii saddexaad. Kokkinakis wuxuu dhaawac ka soo gaaray dhabarka ka dib markii uu ciyaaray finalka Australian Open ee wiilasha taas oo ka reebtay tartanka ilaa bartamihii 2013. Kadib wuxuu ku soo laabtay tartanka isagoo ciyaaraya tartamada mustaqbalka ee Jamhuuriyadda Czech, Kanada iyo Mareykanka oo ay ugu sarreyso wareega afar dhamaadka ee dhacdada Canada F5. Bishii Sebtember iyo Oktoobar, Kokkinakis wuxuu ku tartamay laba tartan oo Challenger ah oo ka dhacay Mareykanka. Markii ugu horreysay waxay ahayd 2013 Napa Valley Challenger halkaas oo uu u qalmay oo uu gaadhay wareegga labaad, isagoo hoos ugu dhacay Bradley Klahn inkasta oo uu hogaaminayay set. Kadib tartankii Sacramento Challenger ee sanadkii 2013 ayuu u soo baxay wareega labaad. Wuxuu mar kale lumiyay inkastoo uu hogaaminayo set ka dhan ah Nick Kyrgios. Natiijo ahaan, qiimeyntiisa ayaa kor u kacday oo ay ku jirtay kaalinta 655aad. Bishii Oktoobar, Kokkinakis wuxuu la midoobay Benjamin Mitchell wuxuuna ku guuleystey Melbourne Challenger isagoo ka adkaaday Alex Bolt iyo Andrew Whittington finalka. Tani waxay sare u qaadday kaalintiisa labiska 453 boos, taas oo u dhigtay inuu xirfaddiisa sare u qaado lambarka 505. Waxa kale oo uu gaaray wareega labaad ee ciyaaraha shaqsiga. Wuxuu u muuqday in uu sababi doono buuq weyn ka dib markii uu qaatay setkii ugu horeeyay ee Matt Ebden ka hor inta uusan lumin labada set ee soo socda. Sanadkii 2013 wuxuu ku soo dhamaaday tartanka Traralgon Challenger halkaas oo uu ku guuldareystay wareegga labaad James Duckworth oo uu ku guuldareystay seddex set oo toos ah.