Griezmann, a €120million signing from Atletico Madrid last year, has found it difficult to hit top form alongside Messi at Camp Nou.
The forward, who missed a penalty against Real Betis last week before scoring in Barca's 5-2 victory, has just two goals, one assist and four chances created to his name in seven LaLiga appearances this season.
Griezmann has previously insisted there are no problems between him and Messi but Eric Olhats, the player's former representative, feels it is telling that the six-time Ballon d'Or winner does not say the same in public.
Speaking to France Football, Olhats even suggested Messi would try neither to speak nor pass to Griezmann when he first joined Barca.
"Antoine arrived at a club where Messi has the final word on everything," he said. "He is as much an emperor as a monarch and he didn't take kindly to the signing of Antoine.
"His attitude has been deplorable and he made him feel unwelcome. I've always disliked hearing Griezmann say that there are no issues with Messi but never the other way around. It's a reign of terror. You're either with him or against him.
"Griezmann is only going to try and solve his problems on the pitch, nothing more. He is never going to look to get into a conflict with anyone. He's not like that at all. And it's not that he lacks personality. He loves football and that's it, he doesn't want to get into arguments with anybody. I've seen him overcome so many difficult moments in his career.
"Last season, when Griezmann arrived, Messi didn't speak to him and didn't pass him the ball. I think he suffered because of a negative adaptation."
Messi came off the bench to lead Barca to victory against Betis, scoring twice and playing a key role in Griezmann's goal when his dummy allowed Jordi Alba's cross to reach his team-mate.
The pair exchanged only four passes in the second half, with Messi mostly combining with Sergi Roberto (15 passes) and Sergio Busquets (19 passes).