Los Blancos' search for a new coach seems to be trickier than first expected, with big names such as Tottenham Hotspur's Mauricio Pochettino and Liverpool's Jurgen Klopp having already been ruled out, according to Marca.
Former Juventus and Italy boss Conte would bring discipline to the side, albeit at the expense of flair.
Zinedine Zidane left his post at the Bernabeu last month after landing his third successive Champions League trophy.
Raul's brilliant relationship with Real Madrid president Florentino Perez is also close.More news: Anthony Bourdains death means loss of a voice for immigrant workers
Guti - who made over 500 appearances for Madrid as a player - was backed by Frenchman Zidane as a future head coach at the capital club in February.
Don Balon report he could have joined Real Madrid for just €60million, which is less than various other outlets are suggesting he'd cost. "He was the coach I wanted here", Galvez said, as quoted by AS.
"Zidane could have resigned a few days later". "Guti called me to thank me for my interest".
Speaking about his former team-mate, Pires believes that it was the right time for Zidane to move on, leaving after achieving unheralded success.