The former France international believes his ex-team-mate can make a success of the position if he takes on the role in the near future
Zidane initially held the role under Jose Mourinho before stepping down to pursue coaching qualifications back September last year, with some reports suggesting the pair had fallen out.
But the 40-year-old has remained on the club's payroll and is now set to return to his previous position once Jose Mourinho has officially left the club and Florentino Perez is re-elected as Madrid president in June.
"He shoulders responsibility well and has an excellent temperament," Pires told RMC Sport. "He knows football by heart."
Paris Saint-Germain coach Carlo Ancelotti is widely expected to replace Mourinho at the Santiago Bernabeu after revealing his desire to leave the club following an approach from los Blancos.
And Pires is convinced that the Italian and Zidane will work in perfect harmony, with his former international team-mate a comforting figure to have by his side.
"If Ancelotti must rely on him in relation to his knowledge then he can be a big help," he added.
"He can be an excellent sporting director. It is up to him to make the decision if he wants the job, but it would be good for French football to see Zidane on a bench again."
Pires, 39, retired from football in 2011 after lifting the World Cup and European Championships with France alongside Zidane.