The former Chelsea manager has been heavily linked with the vacant post at the Bernabeu since Lopetegui's dismissal, however he has officially ruled himself out of the running for the vacant post.
According to 'Sky Sports', Conte has now decided to extend his break from football until the summer.
It is understood that the Italian could be tempted into management mid-season, however does not feel like Real Madrid is the right project for him.
Many had speculated that Conte, 49, would be appointed at the weekend, however it is now believed that Santiago Solari will take charge for the foreseeable future until Florentino Perez names his 13th Real Madrid manager.
Conte's contractual obligations with Chelsea only apply to managing a club in England this season and therefore he would be free to join a club abroad.
Despite the Italian ruling himself out of contention, it was reported that the Real Madrid dressing room, led by Sergio Ramos, were against his proposed appointment.
'The Sun' are still running their story that Tottenham Hotspur manager Mauricio Pochettino tops Real Madrid's wish list.
Real Madrid tried to hire Pochettino in the summer, however he since signed a new five-year deal with the club in May, citing his job in North London as "one of the most exciting jobs in world football".