[1] During his career that spanned from the late 1980s to the mid 2000s, Živković played for Dubočica, Vojvodina, Red Star Belgrade, Sampdoria, and Obilić.
At international level, Živković was capped six times by FR Yugoslavia between 1996 and 1998.
[2] In July 2007, Živković was named the president of his hometown club Dubočica.
[3] In March 2015, Živković was appointed manager of Voždovac.
[4] When Dragan Stojković was appointed head coach of the Serbian national team in March 2021, he brought in Živković as one of three coaches.