The promising striker is keen to stay at his current club and fight for his place despite reports linking him with a move to Arsenal
The Premier League leaders were allegedly keen to sign the Spain Under-21 international on loan until the end of the 2013-14 campaign.
However, Morata has made it clear that a winter move is not an option for him.
"I’m happy here and I feel that Carlo Ancelotti, [Zinedine] Zidane and all of the technical staff have a lot of confidence in me. I’m still only 21 and I want to continue with Madrid for a long time," the striker told reporters.
"Every player always wants to play and the boss has shown that he has faith in me – he has brought me on during difficult games and I am happy to have been able to repay him for the trust he has demonstrated in my abilities.
"I am very happy where I am and I hope to spend many more years with Madrid. Right now, the team is amazing and I think we are currently one of the most dangerous sides in Europe."
Morata's current contract with the Santiago Bernabeu side runs until June 2015.