Savio, 19, arrived from Brescia in January for £5.5million but has failed to make an instant impact at Upton Park after penning a 4½-year deal.
The Hammers head into Saturday's London derby against Tottenham without several key men, including striker Carlton Cole.
But boss Zola reckons Germany Under-20 star Savio is ready to show supporters why he is so highly rated.
Zola said: "We have expectations of him but we can't forget that the boy is only 19.
"He has great potential and he can become a really top player.
"But the crowd and everybody else need to be patient."