Alvarez's departure came as a surprise in 2019 after his close relationship with United's number one shot-stopper and a couple other United players.
The pair also worked together at Atletico Madrid, but it seems the relationship is now broken after Alvarez revealed De Gea signed a new deal without informing him.
"In fact, once De Gea renewed, United put an offer on the table for me. It was me who asked to meet with the club so I could tell them I wanted to leave the club.
"It was at this meeting they asked me to renew. I told them I was going, but not because I wanted to leave United. I wanted to stop coaching De Gea.
"Aside from being his mentor at Atletico Madrid, where I backed him strongly, I was the person who convinced him to sign for United. I was his right-hand man in Manchester.
"I came to United thanks to the great work of Jorge Mendes and because Mourinho wanted to sign me to help David develop and to keep him at the club. At that moment, he wanted to leave United.
"After almost three years with lots of work and meetings with United to renew him and to make him the best-paid player in the world, I learned that he had renewed behind my back. Honestly, it felt like a lack of loyalty.
"During negotiations, he also had a falling-out with the person who had carried out all the talks in order for him to be paid what he was paid. At the last minute, someone else meddled. I insisted that I didn't like that because it seemed disloyal.
"I asked David why he didn't say anything to me and he said that he was told not to say anything to anybody. This had an impact on me. The way I understand my profession is that you can't help someone develop if you do not have total confidence with them and that's why I decided to leave United."