After leaving Red Star halfway through the 1982-83 season, Savić had a six-month stint in La Liga with Sporting de Gijón where he was brought by countryman Vujadin Boškov who was the head coach at the Asturian club.
Savić is married to TV journalist Marina Rajević who hosted a popular one-on-one talk-show Dok anđeli spavaju on RTS' third channel and later on BKTV.
In addition to being a Red Star former great, fondly remembered by football fans across Serbia, Savić unexpectedly grew into somewhat of a pop-culture hero during the late 1990s.
The 1997 movie The Wounds directed by Srđan Dragojević, features a scene with two main characters chanting "Duuuule Savić" during sexual intercourse with a prostitute.
by Radivoj Andrić, 'Lepa sela lepo gore' Savić plays himself as deus ex machina of sorts in a scene featuring the main characters being stranded with a broken down vehicle in the middle of the night.