Alvarez has been a key member of Ole Gunnar Solskjaer’s backroom staff, staying at Old Trafford after Jose Mourinho was sacked last year.
But he has now departed, with Solskjaer extending his gratitude to the former Real Madrid youth goalkeeper.
“I would like to thank Emilio for all his help and hard work since my return to the club.
“We all wish him well for the future,” Solskjaer told the club’s official website.
Alvarez added: “I will always be proud of belonging to this club. Wishing you every success in your endeavours.”
