"Dan" responded in the paper's next day issue with more veiled ridicule of Savićević. In the late 1980s, Savićević married Valentina "Vanja" Brajović. The couple had met and began dating a few years earlier in Titograd while Savićević played for FK Budućnost and teenage Vanja attended the local streamlined touristic high school. Their first child, son Vladimir, was born in November 1989 in Belgrade while Savićević played for Red Star. While living in Belgrade, Savićević and Brajović reportedly resided in an apartment they leased from Serbian professional handballer Svetlana Kitić who had been playing abroad in Italy during that time. Their second child, daughter Tamara, was born in 1992. The couple divorced in 2000. Since the mid-2010s, FSCG president Savićević has been in a relationship with Jelena Babić from Podgorica. His son Vladimir Savićević started his football career at FK Mladost Podgorica youth teams, and was capped for the Montenegrin U19 team. In November 2019, Savićević's daughter Tamara got married to professional footballer Aleksandar Kapisoda, three months after giving birth to their daughter, Savićević's grandchild. Following a Saturday night out in Trebinje on 18 September 2004, Savićević was involved in an incident with Podgorica police several hours later, at around 2:30 am Sunday morning. After driving his Audi TT at a high rate of speed through Podgorica streets and running a red light, he was stopped by a police patrol. According to the police, when stopped, Savićević insulted the policeman with a series of obscenities that among other things included saying: "I'm God, laws don't apply to me". A misdemeanor investigation request (prekršajna prijava) was filed against Savićević by the police. On Thursday, 29 September 2005 at around 5:30pm, Savićević was severely injured in a traffic accident on Stanko Dragojević Boulevard in Podgorica in front of the Montenegrin National Theatre (CNP). The thirty-nine-year-old FSCG president fractured both arms and a pelvic bone after crashing his Yamaha motorcycle into the rear end of a moving Volkswagen Golf Mk4 vehicle driven by thirty-four-year-old Ljubiša Golubović, becoming airborne, and landing hard on the pavement.