Conuicao has just led Milan to the Coppa Italia final after the victory over City Rivals Inter Milan. However, they are also confronted with the prospect of missing a top four and qualifying the Champions League this season.
But Moncada says: “We are not satisfied with the table in the Serie A. We want to do more. It is important to win trophies, and it would be important to win two.
“We want to win the Coppa Italia. It is the only chance to reach Europe, but we want to do more.
“We are very happy (with concuico). He has worked hard in three months and brought an important methodology for Milanello, and we work well together.”
Moncada also confirmed plans to hire a new sports director.
He added: “We are thinking about hiring a sports director to develop the club and bring it to the next level, but our current structure is already important.”