At Juventus, Kovačević found goals in both the Serie A and competitions such as the UEFA Champions League and UEFA Cup becoming their leading European goal scorer, and the top-scorer of the UEFA Cup during the 1999–2000 season, with 10 goals; despite facing competition from the club's starting attacking partnership of Filippo Inzaghi and Alessandro Del Piero, Kovačević made a total of 44 appearances in all competitions in his first season with the club (27 in Serie A, 3 in the Coppa Italia, and 11 in European competitions), scoring 21 goals in all competitions (eight in Serie A, two in the Coppa Italia, and 11 in European competitions, one of which came in Juventus's victorious UEFA Intertoto Cup campaign, which enabled them to qualify for the UEFA Cup). The following season, however, due to the arrival of French striker David Trezeguet, Kovačević found less space in the squad under manager Carlo Ancelotti, making 27 appearances in all competitions (20 of which came in Serie A), mostly from the bench, and scoring only six goals (five in Serie A). The Juventus management felt Kovačević was underachieving and soon both parties were looking for a move out of Italy, with clubs such as Rangers willing to offer £12m for his transfer. In 2001 Kovačević spent a brief time with Lazio (as part-swap deal with Marcelo Salas), making only seven appearances, before moving back to Spain in the middle of the season.