The French midfielder returned to United from Juventus in 2016 in a club-record £89m deal.
He has since struggled to meet expectations at Old Trafford, but Alvarez, who left the club in September, says that has nothing to do with talent.
"I do know that he is a footballer with all the talent to play at any club in the world. Physically he is incredibly gifted," Alvarez told AS.
"Where he has problems is the area of the demands that come with being a star signing. At United, he was weighed down by the responsibility and the pressure of being a multi-million euro signing. He was anxious to show his level.
"I stayed with him after training and did extra work. I can tell you that he has incredible dexterity, talent and is incredible athletically."
On Pogba's future, Alvarez says the World Cup winner would be a 'great signing' for Real Madrid.
"His success depends on his head. He needs to make challenges and to be more self-critical. He could be a great signing for Madrid."