Career
Football Club Groningen
Born in Assen, Živković began playing football at FVV from Foxhol. He was noticed early on due to his agility and speed, and at the age of 11 he left for the youth academy of Football Club Groningen where he progressed. He brought more attention to himself due to his performance for the reserves team, and by the end of 2012 he signed a three-year contract with the club
On the first match day of the 2013-2014 Eredivisie season, on Saturday, 3 August 2013 Živković scored his first regular season goal for the club, thereby relieving Arjen Robben as the youngest to have ever scored for Groningen.
The comparisons with Robben are quickly made. He was subsequently called up for the Netherlands under-19 team
His talent did not go unnoticed, with 11 top football clubs enquiring about him by November 2013, including the likes of Real Madrid and Football Club Barcelona. Ajax
On 17 March 2014 it was officially announced that Živković had agreed to sign for Ajax, taking a three-year contract starting 1 July 2014.
Football Club Groningen also receives Ajax forward Danny Hoesen, as well as a percentage of Živković"s transfer fee should Ajax sell the player before the expiration of his contract, hereby following in the footsteps of Luis Suárez who had transferred from Groningen to Ajax before him.
On 5 June 2014 Živković made his debut for Ajax in a friendly match against Wacker Innsbruck concluding the clubs pre-season trainings camp in Austria. He scored the final goal in the 46th minute of the 5–1 victory. He made his third appearance for the reserves team in another North Holland derby match against neighbouring Football Club Volendam.
The game ended in a 5–0 loss at home.
Živković was sent off receiving a red card in the 59th minute following the ejection of Ajax goalkeeper Peter Leeuwenburgh in the 35th minute of the match. On 28 October 2014, Živković made his regular season debut in the first team, playing in the third round KNVB Cup away match against SV Urk.
Coming on as 46th-minute substitute for Arkadiusz Milik, he scored the final goal in the 89th minute of the 4–0 victory. Scoring on his debut for the first team, Živković became the 50th Ajax player to do so since the introduction of professional football in the Netherlands.
= Willem II On 22 June 2015, it was announced that Živković was sent on loan at Willem II, together with Lesly de Sa and Ruben Ligeon.
On 1 July 2015 he scored the first four goals in a friendly game against Jong Brabant which ended 0-12. Lesley de Sa also added a goal in that game.