The 21-year-old forward had been linked with a loan move to the Emirates Stadium when the transfer window reopens in the new year, but Wenger has moved to play down those suggestions.
Morata has made 12 appearances for Madrid this season but only started one game under new coach Carlo Ancelotti, having come through the club's academy system after joining from Getafe in 2008.
However, speaking ahead of his side's home Premier League clash with Hull City on Wednesday, Arsenal boss Wenger was adamant that there had been no contact between the two clubs regarding Morata's availability.
"No, there is no truth in that," said the Frenchman when asked about the possibility of a move for the Spain Under-21 forward. "I have not been in touch with them (Real Madrid)."
Wenger also used the opportunity to similarly dismiss suggestions of a bid for Corinthians' Alexandre Pato, and he insisted that he is happy with his forward options.
Question marks have been raised about a lack of support for first-choice frontman Olivier Giroud, but the Frenchman feels that he has sufficient depth in his ranks.
"I am not concerned about that (buying a striker in January)," he added. "We have at the moment Yaya Sanogo, who is a striker we brought in during the summer, who is coming back from injury in January.
"Hopefully he will help us in the second part of the season."
