The young forward made inroads into los Blancos first team last term, having come through the ranks at the Santiago Bernabeu.
However, recent speculation has linked him with a move to Liverpool, but Morata insists that he only wants to play for the capital club.
"I'm training well and want to stay in Madrid," Morata said.
"The club and coach want me to stay. I do not have to turn down any offers because I have not received any. I just want to play here.
"It is important to receive minutes and to score goals, and the more minutes you get, the more chances you will score."
Both Cristiano Ronaldo and Gonzalo Higuain stand between Morata and a regular first-team spot and while the 20-year-old believes the Argentine could leave, he is certain the Portuguese will stay put.
"Higuain? It is up to the club, but I see him with the same enthusiasm as always," he added.
"Cristiano? I do not imagine that he will leave. He is the best in the world and has to be on the best team in the world. I am a fan of his."