Morata, 26, joined Atletico in January on an 18-month loan deal, scoring six goals in 17 games for the Spanish side.
He was Chelsea’s record signing when he joined for £60m from Real Madrid on a five-year contract in July 2017, and scored 24 goals in 72 games.
“I am very clear that I want to stay here,” the former Atletico youth player 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.”