The former Italy U21 international joined Valencia on-loan to the end of the season in January.
And Cutrone admits he hopes his future is tied to Los Che, telling AS: "Of course, it is my goal.
"I want to do well on the field to stay, it is what I want.
"As soon as I heard about the interest, I said yes. Nuno also spoke to me great things about the club. I know the importance of Valencia, its history. For different reasons I changed teams several times.
"I want to give Valencia the confidence it gave me, earn my continuity. I am happy. I will give everything to stay here."