During the summer 1985 transfer window, soon to be nineteen-year-old Savićević looked to leave the club in search of a professional contract. 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 look at Savićević's scholarship agreement at Budućnost with a view of examining the legal basis for a possible transfer. Zečević reportedly determined that in order to transfer to Red Star at this time, despite not being under a professional contract with Budućnost, Savićević would still require Budućnost's permission, which the Titograd club was unlikely to give. Another option was for Red Star to financially compensate Budućnost in order to let the player go, however, the Belgrade club was not sufficiently interested in Savićević at this particular time to do that. 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 scholarship agreement expires.