Zenga joined Inter Milan in 1982, after starting his professional career in 1978 in the lower divisions of Italian football (his first team was Salernitana in Serie C1, and he also played for Savona and Sambenedettese). Initially (in the 1982–83 season) he was the substitute of Ivano Bordon, who was one of the top Italian goalkeepers of his era, as he had been Dino Zoff's reserve in the 1982 FIFA World Cup. However, Zenga played Inter's matches in the Coppa Italia, impressing enough that the club decided not to buy another goalkeeper after Bordon's decision to move to Sampdoria during the summer of 1983. Zenga became Inter's starting goalkeeper in the 1983–84 season, where he conceded only 23 goals, better than any other goalkeeper in that season.