While the French coach retains Perez's total support, he will be shown the door if Real finish the campaign without a trophy won.
Don Balon says Germany boss Joachim Low remains Perez's priority target. Low is prepared to return to club football after the summer World Cup in Russia.
Perez also has two alternatives - both based in the Premier League.
Indeed, it's suggested Perez recognises it will be "nigh impossible" to tempt Klopp away from Anfield this summer.