Career
Early years
His first season as senior was with his home town club Radnički Kragujevac during the 2007-2008 season playing back then in the Serbian League West. At the end of that season he moved to the top league club Rad Belgrade entered into the senior team in the 2008-2009. He played as right side midfielder.
Red Star Belgrade
Milivojević signed for Red Star Belgrade on 19 December 2011.
His arrival to Red Star was largely fulfilled by the will of coach Robert Prosinečki, who insisted that Milivojević had bright potential. On 17 November 2012, Milivojević scored an impressive goal against city rivals Partizan.
Anderlecht
On 26 July 2013, Milivojević signed a five-year contract with Belgian football giants R.S.C. Anderlecht. On 1 September 2014, it was announced that Luka Milivojević has joined Olympiacos on loan from Anderlecht.
After the 2013-2014 season, Olympiakos midfielder Luka Milivojević has reiterated his desire to stay at the club
The two clubs may start new negotiations after the season ends and the 24-year-old defensive midfielder has stated that his wish is to make the move permanent. According to reports in Belgium, Olympiakos will meet Anderlecht"s asking price in order to complete the permanent transfer of Luka Milivojević. Olympiakos have been in negotiations with the Belgian club as they were reluctant to pay the €2,7 million Anderlecht have been asking for the 24-year-old Serbian midfielder.
Olympiacos
On 4 June 2015, Anderlecht confirmed that it had reached an agreement with Olympiacos for the permanent transfer of Luka Milivojević.
The Serbian international who has spent a season with the Mauves, joined the Greek champions by signing a four-year contract with Greek champions, on a fee of €2.3 million. He had been called up for the Serbia national football team squad on 29 September 2011, to face Italy and Slovenia in the Union of European Football Associations Euro 2012 qualifying phase.
He made his debut for Serbia on 14 November 2012 in a friendly match with Chile.