Gianni Alessio Bui (born 5 May 1940 in Serramazzoni) is an Italian former professional football manager and player. He played as a forward.
Bui played 11 seasons (188 games, 53 goals) in the Italian Serie A for Lazio, SPAL, Bologna, Verona, Torino, and Milan.
During his managerial career, Bui coached several teams, including Genoa, Chievo, and Venezia.