Gianni Alessio Bui (born May 5, 1940 in Serramazzoni) is an Italian professional football coach and a former player, who played as a forward.
Bui played 11 seasons (188 games, 53 goals) in the Italian Serie A for S.S. Lazio, SPAL 1907, Bologna F.C. 1909, Hellas Verona F.C., Torino Calcio and A.C. Milan.
- Serie A 2nd best scorer: 1968–69 (15 goals) and 9th best scorer: 1971–72 (9 goals).
- Serie B top scorer: 1965–66 (18 goals) and 2nd best scorer: 1966–67 (15 goals).