[1] After a brief stint at Red Star Belgrade, Živković joined Obilić in 1994.
He was a regular member of the team that won the championship in the 1997–98 season.
In 1999, Živković was transferred to Bulgarian club Litex Lovech, alongside Nebojša Jelenković.
After hanging up his boots, Živković started his managerial career at his parent club Radnički Pirot.
From November 2021 to March 2022, Živković served as manager of Omani club Al-Suwaiq.