Marca says should Real finish the campaign potless, Zidane will be asked to resign by the president.
Former Tottenham boss Mauricio Pochettino is Florentino's priority, while Massimiliano Allegri is also under consideration. Like Pochettino, Allegri is a free agent after leaving Juventus last season.
Pochettino has already informed PSG intermediaries not to consider him as a replacement for Thomas Tuchel as he wants to stay clear for the Real job.
Real are still alive in the Champions League, trailing 2-1 in their round 16 tie against Manchester City ahead of next week's second-leg. And they also are two points behind Barcelona at the top of the LaLiga table.