 Zenga akabatana neInter Milan muna 1982, mushure mekutanga basa rake rehunyanzvi muna 1978 mumapoka ezasi enhabvu yeItaly timu yake yekutanga yaive Salernitana muSerie C1, uye akatambawo kuSavona neSambenedettese. Pakutanga mu1982-83mwaka akanga ari mutsivi waIvano Bordon, uyo aiva mumwe wevarindi vepamusoro veItaly munguva yake, sezvo akanga ari Dino Zoffs reserve mu 1982 FIFA World Cup. Zvisinei, Zenga akatamba mitambo yeInter muCoppa Italia, achifadza zvakakwana kuti kirabhu yakasarudza kusatenga mumwe muchengeti wepagedhi mushure mesarudzo yaBordon yekuenda kuSampdoria muzhizha ra1983. Zenga akazova muchengeti wemagariro eInter mumwaka wa198384, kwaakagamuchira zvibodzwa makumi maviri nematatu chete, zvirinani kupfuura chero mumwe muchengeti wemagariro mumwaka iwoyo. 