Last week, Messi stunned the Blaugrana when he sent a fax to club officials detailing his desire to have his contract terminated, which would free him up to move to another team.
The news sent shockwaves through European football, with Manchester City and Inter reportedly leading the way to claim his signature.
Messi's father Jorge met with Barca on Thursday to discuss his son's future, and although no major developments came, it is believed Messi is warming to the idea of remaining at the Camp Nou for another year.
Griezmann, who had an underwhelming debut campaign with Barca, arguably failing to prosper in the shadow of Messi, says he hopes the club captain will stay.
"We are trying to stay updated with the issue, but it is between him and the club," the Frenchman told M6 ahead of his team's Nations League fixtures against Portugal and Croatia.
"We only hope that he stays. I am trying to stay focused on the national team and prepare well for the next two games.
"We have heard a little of everything but we don't know anything else about all this affair."
Griezmann could be set for a more key role with Barca next season regardless of how the Messi saga turns out, as the club have already informed Luis Suarez that he has no future at the Camp Nou.
The Uruguayan is thought to be close to a move to Juventus.