I personally doubt it , Perez has very good relation with him & naturally Mendez but if you understand the dynamics of Real Madrid and how we prefer to present ourselves to the rest of la liga mean we would never open that door to Jose again
Perez is a man who is very successful in having good relation with everyone due to the nature of his business , foes before friends .. his friends extend from Galliani & Silvio to your own presidents .. he had to endure plenty of stick on a personal level due to Jose antics , that's why he didn't take Jose side towards the end his third year and kept Iker in the team despite Jose request to let him go
In Spain appearances matter and Jose character would not allow it , that's why they went for Carlo partly of course due to his great CV especially in the champions league and 2nd and most important is that Perez needed someone to wipe away the damage Jose caused with everyone from his player to other managers to la liga officials .. moreover Perez like any true Madridista would look at the CL record first ... he had a peak Ronaldo and co and managed 3 semi-finals.. Carlo pulled a CL and semi-final spot in 2 years