Career
He has played much of his career in a centre back role, but he has also been used as a right back. Savić began his career with Sartid Smederevo, before transferring to OFK Beograd in June 2000. After five years of playing in the Serbian Superliga, he was signed by Spartak Varna in the summer of 2002.
Spartak Varna
Savić made his Bulgarian A PFG debut on 10 August 2002, replacing Stefan Donchev in a 3–1 away loss against CSKA Sofia.
Seven days later, he made his first start for Spartak, in a 1–0 loss against Lokomotiv Plovdiv at Spartak Stadium. On 24 February 2004, Savić scored an own goal in a 2–1 home loss against Cherno More in the derby of Varna.
Lokomotiv Sofia
On 3 September 2004, Savić joined Lokomotiv Sofia on a free transfer. He made his first league appearance for Lokomotiv in the 4–0 defeat by Lokomotiv Plovdiv on 11 September.
On 31 May Savić was sent off in a match against his previous side Spartak Varna for a foul on Angel Stoykov.
On 11 April 2011, Savić became the second foreign player after Nebojša Jelenković, who made 200 appearances in the Bulgarian A PFG. lieutenant was announced on 10 June 2011 that, along with Valentin Galev, Kristian Dobrev, Marcho Dafchev and Rumen Goranov, Savić had agreed to sign a new two-year contract, which would keep him with Lokomotiv until 2013. The contract was finally signed on 19 June. On 9 February 2012, his contract with Lokomotiv was terminated.
Botev Vratsa
On 14 February 2012, Savić joined Botev Vratsa.
He made his debut for Botev in a 1–0 home loss against Slavia Sofia on 3 March.