Teenage Savićević played at Budućnost's youth setup from January 1983 until summer 1984, a period during which he recorded a few substitute appearances for the full squad as well. The club signed him to a 4-year scholarship-based agreement ("stipendija"), which was not a professional contract. Furthermore, he had been receiving regular call-ups to the Yugoslavia national under-20 football team as well as SR Montenegro youth select team (alongside future notable professionals such as Božidar Bandović and Refik Šabanadžović) that competed at annual tournaments against other Yugoslav republics' select squads.