Pogba has endured a difficult season at Old Trafford, where a series of poor displays from the Red Devils saw them end their Premier League campaign in sixth place - and culminated in the 26-year-old remonstrating with fans after their final day defeat at home to Cardiff.
Despite this clash with his own supporters, Griezmann revealed in his new book Getting To The Top Of World Football that the United midfielder is a good person who is treated unfairly by the press.
As reported by the Manchester Evening News, Griezmann said: "Paul is a great guy [but] because of his over-exposure in the media, his transfer fee and his spectacular style of play, everything he does is scrutinised.
"The press is very demanding with him, sometimes too harsh in my opinion. You can get the feeling that everything just slides off him, but it’s not the case."
The World Cup winner went on to suggest that if Pogba is given more encouragement from the press, he has the potential to win the biggest individual honour in the game.
Griezmann added: "He’s someone who needs to feel loved. The media, even though they are doing their job, should encourage this more.
"He doesn’t get the recognition he deserves. Paul has the potential to win the Ballon d’Or one day."
Rumours are circulating that Pogba will leave United this summer to join Real Madrid but if he does go to the Spanish capital, he will not be living near his France colleague, after Griezmann recently revealed his decision to leave Atletico Madrid.
He is expected to join Barcelona in a deal worth over £100m when the transfer window opens, despite rejecting the chance to join the Catalan club last year.