The winger joined from Fiorentina last month in a £22 million move after impressing at last summer's World Cup and in Serie A this season, notching four goals and four assists for the Viola in 2014-15.
Cuadrado made his Chelsea debut in the 2-1 win over Aston Villa on Saturday, coming on for the final 10 minutes, and Mourinho expects his transition to English football to take some time.
"He is selected [for the Everton match]," Mourinho told the club's official website. "I know if he will start or not, but I won't say.
"It's normal, step by step, to be integrated. He needs time. I know Italy and I know the difference between Italy and England. His formation, his development, his experience – everything was in Italy.
"I wasn't expecting him to come on to the pitch against Aston Villa and destroy them. Stability, time, integration – I think we will see the best Cuadrado next year."