Collovati was born in Teor, in the province of Udine. Brought up through the A.C. Milan youth academy, he debuted in Serie A with the "rossoneri" in the 1976–77 season, in which he played eleven times and even won the Coppa Italia. In the next season he played more regularly (25 appearances, 1 goal) but his definitive moment came during the 1978–79 season in which, thanks to his 27 appearances, he won the "scudetto". Following the 1979–80 season, Milan was relegated to the Serie B for their involvement in the Totonero football betting scandal. Unlike other players, Collovati stayed on with Milan in Serie B and played 36 games scoring two goals, winning the league title that season, and helping the club to regain promotion to Serie A the following season. Back in Serie A the next season, Milan won the Mitropa Cup with Collovati serving as the team's captain: however Milan was relegated to Serie B once again, but this time for their on-field exploits. On this occasion, Collovati (who in the meantime was called up to the "Nazionale") decided to join local rivals Inter Milan.