Zeljković started playing football in his hometown of
Žalec. He went on to play for the youth teams of several Slovenian football clubs, including
Maribor,
Celje and
Olimpija Ljubljana. Zeljković joined Slovak club
Spartak Trnava in July 2023, signing a four-year contract. On 12 May 2025, Zeljković signed a four-year contract with
Czech First League club
Viktoria Plzeň for a reported transfer fee of €1.5 million. He made his European debut for the club in a 3–1 win over
Servette, where he got
sent off in the 66th minute. On 3 February 2026, Zeljković joined
MTK Budapest on a half-year loan deal with an option to make the transfer permanent. ==International career==