Morata, who turned 23 last month, joined the Italian champions in July last year for a fee of 20 million euros (14 million pounds) and scored some crucial goals as Juve won a domestic double and reached the Champions League final.
Real have been struggling to find the net under new coach Rafa Benitez and Cristiano Ronaldo's run of poor form together with Karim Benzema's legal problems have prompted speculation they could move for Morata in January.
It is unclear whether any repurchase clause was included in the deal for the Spain international, whose Juve contract runs until 2019.
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Speaking on Spanish radio late on Sunday, Morata said the only communication he has had with Real were messages of support from club director Emilio Butragueno.
"A return to Madrid is something I cannot think about," he told Onda Cero. "It would be showing a lack of respect to Juventus, they paid a very high price for me.
"They put their faith in a lad who had played on and off for Real Madrid instead of (putting it) in the leading scorer of a top European league."
A product of Real's youth academy, Madrid-born Morata spent most of the time on the bench under former coaches Jose Mourinho and Carlo Ancelotti and said he had needed a change.
He scored once in each leg of the Champions League semi-finals last term to help knock Real out 3-2 on aggregate and netted Juve's equaliser in the final before they lost 3-1 to Barcelona.
"When you leave Madrid it's tough, it's hard to leave it behind, all the more so when you are a Madrid fan.
"But I am at a club that makes me very happy. I am dealing with it in the sense that if they are asking me about Madrid it's because I am playing well and scoring goals."
(Writing by Iain Rogers; Editing by John O'Brien)
