The Segunda supremo - who is also a full Blancos member - is not impressed with both the the Portuguese's demeanour and the way he conducts his business in the Spanish capital
The Segunda Liga patron is also a full member of the Spanish champions, and he feels the trainer's reluctance to develop youth players is holding the club back, while he is not a fan of the 49-year-old's attitude towards the country's media.
"I think Real Madrid need to replace Mourinho with another type of coach because enough is enough," Gonzalez said to Onda Cero Catalunya.
"Things have gone full-circle. A few years ago, Real Madrid had looked to use the youth team, while Barcelona signed the big names such as [Diego] Maradona and [Johan] Cruyff and Real's successes are there to see.
"Now it is us – Real Madrid – who bring in the star players and Barcelona who use their youth team. Look at the success it's brought them.
"It all annoys me. The image of our club is disastrous. We are making more enemies than friends. Not looking to use the youth team is a tremendous mistake."
Gonzalez's Cordoba are currently preparing for the Copa del Rey match against Madrid's arch-rivals Barcelona.