[1] Born in Belgrade,[2] Vučičević was with Dorćol and OFK Beograd youth selections,[3] before he a scholarship contract FK Čukarički.
[4] In summer 2016, Vučićević signed his first four-year professional contract with Red Star Belgrade,[5] but due to administrative problems[6] he failed to play with new club until November same year.
He made his professional debut in 36 fixture of the 2016–17 Serbian SuperLiga season under coach Boško Gjurovski, replacing Srđan Plavšić in 71 minute of the match against Javor Ivanjica, played on 17 May 2017.
[11] After the end of the first half-season in the domestic competition, a loan deal was mutually terminated and Vučićević returned to Red Star Belgrade.
In a period while his father, Nebojša, trained him as a coach in OFK Beograd youth academy, he started using Vanja as a centre forward.