Eric Olhats used to look after the former Real Sociedad and Atletico Madrid forward, and he believes that Griezmann is attempting to create a positive atmosphere within the Barcelona dressing room.
But he feels that Messi's power within the organisation and the fact that he was not pleased with Griezmann's arrival has hade the situation very difficult.
Olhats said to France Football: "Antoine arrived at a club with serious problems where Messi controls everything. He is both emperor and monarch and wasn't happy with Antoine's arrival.
"His attitude has been deplorable, it has made him feel [displeasure]. I have always heard Antoine say that he had no problems with Messi, but never the other way around.
"It is the regime of terror. Either you are with him, or you are against him."
Olhats added that perhaps Griezmann's inherently positive outlook is counting against him in that he does not want to cause any further issue with Messi that could damage their relationship.
He stated: "Griezmann is only going to try to solve his problems on the field, nothing more. He will never enter into conflict with anyone. He is not like that, at all. And it is not for lack of courage or personality,
"He loves football and nothing else, he does not want to get into disputes with anyone. As soon as he is on the field, he is happy. For him, it is useless to go to battle."
Messi's dictatorial style is well-known and his run-in with coach Quique Setien at the end of last season ultimately led to his demise.