The Italian was linked with the role after the sacking of Julen Lopetegui following Real's 5-1 thrashing at the hands of Barcelona at the weekend, Sky Sports reported.
Conte left Chelsea in July and has now decided to extend his break from football until the summer.
However, he could be tempted into management mid-season, but only if the project was right.
As Sky Sports News reported last week, Conte's contractual obligations with Chelsea only apply to managing a club in England this season and therefore he is free to join a club abroad.
Santiago Solari has been placed in temporary charge of the Madrid giant.
Spanish league rules mean the 42-year-old Solari can only manage on an interim basis for two weeks, at which point Real must appoint a permanent successor to Lopetegui.