Ogbonna knows the qualities Zaza can bring to the Hammers having played alongside him for Italy and feels he was starting to show his qualities in the 1-0 victory over Crystal Palace last weekend.
The Hammers defender can still remember the time he took to adapt to his new surroundings in England following his move last summer and feels it is the same for Zaza.
But having earned such high praise from his manager Slaven Bilic and several of his team-mates, Ogbonna sees no reason why Zaza cannot grown even stronger and says it would be great for him to score his first goal when the Hammers face Sunderland at London Stadium on Saturday.
Ogbonna said: “I think the goal is coming for Simone. We have to give him some time because he has changed leagues and has arrived from Italy into England.
“When I first came here it was not easy and maybe he needs time to adapt. He had a really good performance last weekend and showed what he can do.
“He just needs a goal now and maybe he can get that in front of our fans at London Stadium.”
The victory over Palace last weekend helped move West Ham out of the bottom three, but Ogbonna says this is just the start and hopes the team can now force their way into the top half of the table.
The experienced defender would love to record another victory at the Hammers new home and make up for the recent disappointments against Watford and Southampton at London Stadium.
Ogbonna added: “This game is very important for us. The Premier League is like no other league and there are no easy games. We have to be focused and perform like we did in the last game.
“The London Stadium feels like our home and it is normal that it will take time. We have been unlucky in some of the games and now we need to look forward. Hopefully we can get a victory on Saturday.
“We feel that the pressure has come off us a little bit and we had a really good performance against Crystal Palace last weekend.
“We have now got many players back from injury and important players like Aaron Cresswell, Manuel Lanzini and Dimitri Payet.
“It helps the team so much because they can keep the ball and can get the ball through to Zaza. It was a really good performance from us last week.”
With Aaron Cresswell ruled out through suspension, one of the options for Slaven Bilic could be using Ogbonna as a makeshift left-back – something which is not new to the Italian defender.
“I have played the full-back position at Juventus so it is not difficult for me and I can adapt. I have to do my best for the team.”