Vasic first joined Padova's academy in 2011: he then spent a season-long loan at Cittadella before coming through his parent club's youth ranks.[2][3][4] Having been promoted to Padova's first team at the start of the 2020–21 season, under head coach Andrea Mandorlini,[4][5] he made his professional debut for the club on 30 September 2020, starting in a 3–1 away win over Frosinone in the Coppa Italia.[5][6]
On 31 January 2022, Vasic extended his contract with Padova until 2026 and was subsequently loaned to fellow Serie C side Lecco for the remainder of the season.[3][7]
On 17 September 2022, Vasic scored his first professional goal in a 3–0 league win over Pro Patria.[8][9] During the 2022–23 season, he established himself as a regular starter and one of the most valuable performers of his side,[3][4][10] having scored eight goals and four assists in 37 league matches;[5][10] however Padova was eventually eliminated by Virtus Verona in the second round of the playoffs.[11]
On 5 July 2023, Vasic officially joined Serie B side Palermo for a reported fee of two million euros, plus add-ons,[12] signing a five-year contract with the club.[12][13]
Despite playing as a forward at the start of his youth career, Vasic was moved to the mezzala role a few years before his professional debut.[4][5] He has been regarded for his physical attributes and his athleticism,[5] as well as his ability in aerial duels and his off-the-ball movements.[4][5]