The 26-year-old striker joined Atletico on an 18-month loan deal from Chelsea in January, and has caught the eye when chipping in with six goals in 17 appearances.
It remains to be seen whether he will be recalled by his parent club, and there has even been talk of Atleti sending him back, but as far as Morata is concerned, he wants to stay.
"I am very clear that I want to stay here," he told Spanish sports newspaper Marca. "Leaving here has not crossed my mind. I want it to be resolved as soon as possible. I'm happy here. I want to be here for all the years I have left as a professional.
"If it was solely down to me, I would have signed my contract with Atletico. It's what I want, but there are contract matters. I did everything possible to come here and I will do my best to stay."