Messi, 33, was met by a pack of journalists at El Prat airport in Barcelona on Wednesday upon his return from international duty with Argentina.
He was asked him what he thought about Eric Olhats' claim last week that he had too much control at Barca and had failed to help accommodate Griezmann at the club.
"I am tired of always being the problem with everything that goes on at this club," Messi said.
Griezmann has always maintained that his relationship with Messi is good and sources close to the France international say it has been years since he spoke with Olhats.
The two combined to good effect on the pitch in Barca's final game before the international break, with Messi's dummy setting up a goal for Griezmann.
But Messi's latest comments will only increase speculation that he could leave Barca when his contract ends next summer.
Speaking in September, Messi, who has been at Barca for 20 years, said his main problem was with former president Josep Maria Bartomeu and his management of the club over the past few years.
But Bartomeu resigned in October, paving the way for his successor to open talks with Messi over a new deal.
A new president will not be elected until late January and their first task will be to convince Messi that they can build a winning team around him for the final years of his career.
As things stand, Messi will be able to negotiate a pre-contract with any club in January and can leave for free next June.
"When you are lucky enough to have the best player in the world in your team, you need to retain that talent," said Victor Font, one of the candidates for the presidency, in an interview with Reuters.
"If Messi goes to a competitor we will not find an alternative easily as there is no alternative to Messi. So that's why retaining him in the short term is critical."
He will return to training with Barca on Thursday ahead of Saturday's game against unbeaten Atletico Madrid, who will be without his close friend and former teammate Luis Suarez after he tested positive for the coronavirus.