Born in Guinea-Bissau, Fati also had the option to represent Portugal at international level but he chose to play for La Roja and this week he was granted Spanish citizenship.
Fati was then added to the Spain Under-21 squad to face Montenegro after Barcelona team-mate Carles Perez withdrew through injury.
Moreno indicated Fati is already in his thinking as Spain work towards Euro 2020, with qualification in sight after six wins from six in Group F.
"Of course I would like Ansu to be here," he said ahead of Saturday's trip to Norway. "We had him in the pre-list.
"He has broken the system of the age groups. We believe it is important to have players who have a goal.
"If he starts scoring goals and breaking out we will not give up having such a player with us.
"All good guys are welcome. Ansu has shown many things.
"Of course it would be feasible for him to be at the Euros."
Moreno's contract expires after Euro 2020, the coach having taken charge on an initial temporary basis after Luis Enrique had to step away for personal reasons.
Although he is yet to open talks with the Royal Spanish Football Federation over a renewal, Moreno is not concerned about the situation.
"I had not thought about it. They have neither spoken to me nor do I want them to talk to me," he added.
"We are focused on getting 30 points. It does not give me any value to be told about it.
"This is a lot of fun and every week something new appears to entertain you. I am happy with how things are going. I have not seen them yet in losing.
"Hopefully we can secure qualification, I would like to do it by winning all the matches."