Real are back in the title hunt after Barcelona's recent stumbles and directors are excited about their prospects this season.
But El Confidencial says Perez has his doubts, particularly with the way Ancelotti rotates his players.
The Real president would prefer the Italian settle on a first-choice XI, particularly with his midfield.
Perez fears Ancelotti struggles to make the hard decisions when dropping players, citing the treatment of the rebellious Angel di Maria as an example to confidants.
Senior Real players are aware of Perez's concerns, but during their warm weather training camp in Doha, moved to assure the president about team morale and their title belief.
"This is our Liga," the players are now saying as a mantra around the club.
But Perez still has his nagging doubts about the man in charge.
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