After beginning his professional career with hometown side Budućnost in Yugoslavia, Savićević moved to the more established Yugoslav First League club Red Star Belgrade in 1988 where he became prominent part of the team that won the 1990–91 European Cup—coming second in the 1991 Ballon d’Or voting—before making a big money transfer to Italian champions AC Milan in 1992.

With a new coach in addition to two established player acquisitions—goalkeeper Rade Zalad from Partizan and striker Radomir Savić who arrived from Spartak Subotica having previously attained some big match pedigree at Red Star Belgrade and FK Sarajevo—expectations were raised.

To that end, he went to Red Star Belgrade on his own initiative and got to the club's technical director Dragan Džajić who in turn had former referee Konstantin Zečević [fr] look at Savićević's stipend agreement at Budućnost with a view of examining the legal basis for a possible transfer.

As a parting bit of career advice on this occasion, Džajić reportedly counseled Savićević not to sign a professional contract with Budućnost at all and then come to Red Star two years later in 1987 on a free transfer once his stipend agreement expires.

Wanting the security of a professional contract, Savićević continued pursuing it, going straight to Nikšić the same summer and getting a verbal commitment from FK Sutjeska that seemed ready to pay a large sum to Budućnost in order to have the talented youngster.

Similarly, in the Marshal Tito Cup, after initially eliminating the 4th-tier Neretva Metković followed by overcoming the First League rivals Velež Mostar in a hard-fought two-legged tie (4-3 on aggregate) in the round of 16, and finally beating Radnički Kragujevac in the quarterfinals, each win coming throughout the fall of 1986, Budućnost eagerly awaited its semifinal clash versus Rijeka set for March and April 1987.

Though the player had often had issues with Budućnost's club management in the past, often openly stating so in Yugoslav sports media, this relationship further deteriorated when one of the main stipulations of his professional contract with the club—that of being given a two-bedroom apartment by summer 1987—was not met within the agreed-upon timeframe.

Already talking to Red Star's Montenegro-born scout Nastadin Begović who had family in the Titograd area and often checked in on the young player whenever in town, Savićević wanted out of Budućnost and, via his media statements, began putting pressure on the club to sell him immediately.

Savićević stated in later interviews that the personal relationship he had developed with Begović, and eventually Slijepčević, as well as Red Star's offer being "direct and financially more concrete than Partizan's" ultimately swung his decision where to continue his footballing career.

[7] In late March 1988, Hajduk Split also joined the chase for Savićević's signature and, according to the player's claims in later interviews, offered the largest sum of money of the three suitors, but he still decided to honour his preliminary agreement with Red Star.

Barely a few days after signing with Red Star Belgrade, twenty-one-year-old Savićević promptly was called in to serve the mandatory Yugoslav People's Army (JNA) stint that would keep him out of action for the entire 1988–89 league season.

JNA soldier Savićević, still stationed in the city of Skopje, was approved a leave to make his competitive debut for Red Star during early October 1988 in the return leg of the European Cup first-round clash versus Irish champions Dundalk.

The player had reportedly been on the club's radar for more than a season, with Milan's sporting director Ariedo Braida coming to Belgrade in April 1991 to personally assess him at the European Cup semi-final return leg versus Bayern.

To cap off the frustrating season, in late May 1993, Savićević was not included in the team Capello took to Munich to face Olympique de Marseille in the 1993 UEFA Champions League Final as the three foreigners chosen were van Basten, Rijkaard, and Papin.

His main two attacking midfield competitors Gullit and Van Basten were gone; the former transferring to Sampdoria frustrated at seeing his role at Milan greatly reduced and the latter taking a year off to heal his ankle injury that would eventually turn out to be career-ending.

Then, in mid-December 1993, the row deepened when Capello dropped him from the squad altogether for the 1993 Intercontinental Cup in Tokyo versus Telê Santana's São Paulo, choosing Papin, freshly arrived Marcel Desailly, and Răducioiu as the three matchday foreigners.

[30] Still, despite smoothly finishing top of the group and easily winning the one-match semifinal, Milan was in a bit of disarray heading into the final as both central defenders Franco Baresi and Alessandro Costacurta, the core of Capello's tactical defensive setup, were suspended.

The sheer audacity and technical brilliance of the goal – decision to go for a well-placed lob from the right edge of the penalty area on Barca goalkeeper Andoni Zubizarreta who was slightly off his line in a situation when most would get closer and opt for a hard-driven shot as no defender was near – won Savićević much praise and accolades.

[34] Speaking to Galiani from a vacation, Savićević was reportedly vehemently against both proposed moves due to increasing the number of squad foreigners to five or six thus limiting his playing opportunities, even telling Galliani that if Ginola and Asprilla are brought in he would not show up for training camp and would be seeking to be transferred out of the club.

[36] Despite the team's mid-table Serie A form in 1995, Savićević continually played well for the rossoneri in the Champions League en route to their third successive final that, for him, culminated in a spectacular semi-final versus Paris Saint-Germain, where he scored twice in the return leg at San Siro.

In spite of his skill and success with Milan, he was also criticized in the Italian media during his time with the club for his poor work rate and lack of consistency, in particular for not always running or trying against smaller teams, and his performances regularly blew hot and cold.

Within months, furious over lack of playing time and overall status in the national team, young Savićević began viciously criticizing Osim in the Yugoslav press, questioning the coach's expertise and even professional integrity.

In a February 1987 interview for the Duga magazine, twenty-year-old FK Budućnost attacking midfielder Savićević launched a blistering broadside at the Yugoslavia head coach: Had I been playing my club football at Željezničar, I'd be a national team regular right now.

Then, a month later—perhaps surprisingly knowing the coach's conservative nature—Osim brought on the JNA soldier Savićević (who was also coming off a great performance in Red Star's European Cup tie versus Milan) as a 69th-minute sub for Bora Cvetković right after France went ahead 1–2 a minute earlier on a goal by Franck Sauzée.

The following qualifier in late April 1989 was a crucial one away at France and Osim decided not to play Savićević, choosing instead to continue with his older regulars up front such as Zlatko Vujović, Sušić, and Baždarević as Yugoslavia eked out a hard-fought scoreless draw at the Parc des Princes.

Heading into the World Cup, Savićević's chances of playing a larger national team role looked to have received a bit of a boost as Mehmed Baždarević, one of his competitors for an attacking midfield spot, was suspended by FIFA for spitting at the Turkish referee Yusuf Namoğlu during the crucial qualifier versus Norway.

Playing in front of almost 75,000 fans (the largest crowd of the entire 1990 FIFA World Cup), the team was picked apart by the speed and strength of the German players as Lothar Matthäus and Jürgen Klinsmann had the Elf 2–0 up before halftime.

In the knockout stages, Savićević was again on the bench for the start of the match against Spain in the excruciating late afternoon heat of Verona, but got his chance early into the second half with the score still tied at 0–0, coming on for largely ineffective club teammate Darko Pančev.

[122] Others, like FK Partizan vice-president Ratomir Babić, accused Savićević of "scoring political points for his mentors in the separatist-oriented Montenegrin regime by intentionally spreading explosive false rumours in order to bring the union's league into disrepute".

[163] 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.