Zidane is expected to step down from his role as Madrid boss for a second time at the end of this season, despite still having a year remaining on his contract.
The Frenchman has reportedly already told his players that he will not see out his current deal, although Zidane has since denied those rumours.
Nevertheless, Real Madrid are understood to have drawn up a shortlist of candidates to replace Zidane, including Raul, Massimiliano Allegri and Carlo Ancelotti.
Spanish outlet AS reports that Los Blancos have already held initial talks with Raul on matters such as staffing and methods of working.
The Spaniard is currently in charge of Real Madrid Castilla, who play in the third tier of Spanish football, and reportedly wants to focus on promoting youth should he get the top job at the club.
German outfit Eintracht Frankfurt are also thought to be interested in appointing Raul, although he would prefer to take over at the Bernabeu, having represented Real Madrid for 18 years as a player.
The 43-year-old is Real Madrid's second-highest scorer of all time, netting 323 goals in 741 games for the club across all competitions.