Career
Živković represented his country at every level from Under-17 to Under-21. After starting out with his hometown club Sloboda Užice, Živković joined the youth system of Partizan in 2005. He was subsequently promoted to their first team in the spring of 2007, before signing his first professional contract with the club on 1 June 2007, on a five-year deal.
Živković initially played for Teleoptik, before returning to Partizan.
In the summer of 2008, in order to gain more playing time and experience, Živković was sent on loan to Metalac Gornji Milanovac. He immediately became the first-choice goalkeeper in his first season at the club, as they got promoted to the Serbian SuperLiga.
In the following season, the club"s first in the top flight, Živković missed only one out of 30 games, helping his team avoid relegation. In the summer of 2010, Živković returned to Partizan, being projected as a backup goalkeeper to Radiša Ilić.
He dropped out of the 18-man squad after Vladimir Stojković joined the club in late August 2010.
Eventually, Živković made one league and one cup appearance in the 2010-2011 season. He was again loaned to Metalac Gornji Milanovac in the summer of 2011, making 13 league appearances in the 2011-2012 season. After leaving Gornji Milanovac for the second time, Živković started the 2012-2013 campaign at Teleoptik, before being promoted back to Partizan in October 2012, as a replacement for the injured Vladimir Stojković.
In the following season, Živković made his debut in Union of European Football Associations competitions, coming on as a substitute for the injured Milan Lukač in the second leg of the Champions League third qualifying round versus Ludogorets Razgrad on 6 August 2013.
He managed to make four league appearances in the 2013-2014 season. In the fall of 2014, Živković was still the second-choice goalkeeper to Milan Lukač.
Živković represented Serbia and Montenegro at the 2006 Union of European Football Associations Under-17 Championship, together with his club teammates Stevan Jovetić and Nikola Gulan, among others He then represented Serbia at the 2007 Union of European Football Associations Under-19 Championship.
In the meantime, Živković made his debut for the Serbian national under-21 team in a 6–2 home friendly victory over Cyprus U21 on 15 May 2007.
On 30 May 2015, following his performances at club level, Živković received his first call-up for the Serbian national team
