Conceicao has just guided Milan into the Coppa Italia final after victory over city rivals Inter Milan. However, they also face the prospect of missing a top four finish and Champions League qualification this season.
But Moncada says:“We are not satisfied with the table in Serie A. We want to do more. It’s important to win trophies, and it would be important to win two.
“We want to win the Coppa Italia. It’s the only chance to reach Europe, but we want to do more.
“We are very happy (with Conceico). He’s worked hard in three months, bringing an important methodology to Milanello, and we work well together."
Moncada also confirmed plans to hire a new sporting director.
He added, “We think about hiring a sporting director to develop the club and take it to the next level, but our current structure is already important.”