[3] Živković made his senior debuts at his hometown club Radnički Niš, aged 16, which attracted the attention of Partizan.
Over the next three seasons, Živković played regularly for the side, making 75 league appearances and scoring six goals.
After two seasons with the Građevinari, Živković moved abroad to Japan and joined Júbilo Iwata in mid-2000.
He also played with OFK Beograd and Voždovac, before going abroad for the second time and joining Shandong Luneng in early 2006.
He also represented Serbia at the 2008 Summer Olympics as one of the three over-age players alongside Miljan Mrdaković and Vladimir Stojković.