Veselinović progressed through the youth system of Partizan as one of the club's most promising prospects, breaking into the first-team squad under manager Lothar Matthäus in the second half of the 2002–03 season.[1] He was later assigned to their affiliated club Teleoptik on dual registration, racking up an impressive goals-to-games ratio in the Serbian League Belgrade. In early 2005, Veselinović was loaned to Obilić until the end of the season. He scored five goals in 11 league appearances and helped the side narrowly avoid relegation from the top flight. After returning to Partizan in the 2005–06 season, Veselinović again struggled to receive more playing time, but continued to score regularly for Teleoptik in the Serbian League Belgrade. He later also went on loan to Bežanija and Beira-Mar.