His first senior club was FK IMT, playing in the Serbian League Belgrade (third national tier), for which he made his debut in the 2015–16 season.
On 19 January 2020, he was loaned to Polish Ekstraklasa club Wisła Kraków for the rest of the season with an option to buy.
[3] On 28 May 2020, it was confirmed that the Polish club had triggered the option and Kuveljić signed a permanent deal until June 2023.
[5] The move was made permanent on 18 April 2023, when TSC Bačka Topola exercised their buy clause.
[6] Having made just one appearance for TSC across the 2024–25 season due to an injury, on 9 January 2025 he signed for Spartak Subotica on a two-and-a-half-year deal.