Florentino, according to Mundo Deportivo's Francesc Aguilar, is weighing up his options as the season comes to an end.
It's suggested he is growing tired in the position and is seriously considering resigning.
Aguilar posted to social media: "I know it is hard to believe, but a very trustworthy source reveals to me that Florentino Pérez is once again very unhappy in his tenure as president of Real Madrid and is considering leaving.
"It does not mean, surely, that he throws in the towel again, but he is very unhappy. He's thinking about it."
Apart from a spell away from the club between 2006 and 2009, Florentino has been president of Real Madrid since 2000.