The 21-year-old has only made one league start this season and reports had suggested he is a transfer target for Arsenal manager Arsene Wenger during the January transfer window.
Morata came off the bench to score Real's fifth goal against Real Betis on Saturday, his third league goal of the season, and after the game was adamant that his future lies in the Spanish capital.
"Despite everything that is being said, I'm happy here. I want to stay," he said.
"I have spoken with the coach and the club, and I talk every day with my team-mates.
"If I have to help by playing a few minutes here and there, I'll do it, but it’s even better if I get a few more.
"There are a lot of things being said, but I want to stay here and keep working hard and improving. I have been at this club for my whole life and it is the best in the world.
"The best are here and I want to help when I am needed."
