Kosović was born in Belgrade, SR Bosnia and Herzegovina, SFR Yugoslavia to a Bosnian-Serb family.

In 2007, he went back to Trebinje where he became an assistant coach for his former team Leotar of the Basketball Championship of Bosnia and Herzegovina.

[1] In the late 2000s and early 2010s, Kosović was a coach at the Bodiroga Basketball Camp in Trebinje.

[2] Since then he has been a part of coaching staffs of the Zvezda head coaches, as follows Svetislav Pešić, Milivoje Lazić, Vlada Vukoičić, Dejan Radonjić, Dušan Alimpijević, Milenko Topić, Milan Tomić, Andrija Gavrilović, Dragan Šakota, and Saša Obradović.

In August 2022, Kosović was named an assistant coach for the Serbia national team under Svetislav Pešić.