Savić was eight years old when he began training for the Red Star Belgrade, where he passed all age categories.

[4] In 2015, Savić joined Sheriff Tiraspol, where he made a total of 40 appearances and 4 goals in all competitions over two seasons.

[6] In his first season back in Belgrade, Red Star became the first team in history to make it to the 2018 Europa League knockout phase from the first qualifying round.

[7] During the 2017 season, coach Vladan Milojević played Savić in reputable defensive partnerships with Srđan Babić[7] and Damien Le Tallec.

[7] In May 2018, Savić was elected in the best 11 players for the 2017–18 Serbian SuperLiga season, by clubs captains' and managers' choice.

During the qualifying rounds, playing mostly in tandem with Miloš Degenek, Red Star managed to concede only three goals.

In March 2018, Savić got a first call to the Serbia national football team under coach Mladen Krstajić, for friendly games against Morocco and Nigeria.