Born in Novi Banovci,[2] Kukolj passed FK Partizan youth school. made his professional debut for Partizan in the last fixture match of 2014–15 Serbian SuperLiga season against Borac Čačak, played on 24 May 2015.[6] After 2015–16 season he had spent with youth team, Kukolj signed a three-year professional contract with Partizan[7] and moved to Serbian First League side Bežanija on one-year loan closely.[8] As he spent the first season match sitting on the bench[9] and missed next 2 matches, loan was terminated and Kukolj returned to Partizan in last days of the summer transfer window 2016.[10] In the winter break off-season, Kukolj was loaned to the Serbian League Belgrade side IMT, and shortly after he was nominated for the best young player of the tournament "Čukarica 2017".[11] In summer 2017, Kukolj was loaned to Dinamo 1945, where he played in the Serbian League Vojvodina as a bonus player for a half-season.[12] He also moved on loan to the Serbian First League club Budućnost Dobanovci until the end of the 2017–18 campaign.[4]