Griezmann has told close friends he wants to stay loyal to Diego Simeone and will sign a new contract with Atletico but Messi thinks Barca should not give up hope.
The midfielder's representatives look set to meet with Arsenal officials this week.
Griezmann, 27, is still to decide whether to join Barca in a €100 million move or remain at Atletico, with the France global saying he expects to make a final decision ahead of this summer's World Cup.
"It is easy to get along with great players, and Griezmann is one of the best", Messi said.
Griezmann is a great player, claims Messi.
"He's going through an exceptional moment in his career". Aside from increasing his buyout clause it would also see Griezmann recieve a huge pay rise, earning €23m per season.
France's midfielder Paul Pogba (R) and France's forward Antoine Griezmann attend in a training session at the Friends Arena in Solna on June 8, 2017, on the eve of the FIFA World Cup 2018 qualifying football match Sweden.
Lionel Messi has publicly supported Barcelona's move to sign Antoine Griezmann from Atletico Madrid this summer.
It appears a decision has yet to be made by Griezmann, and with the World Cup coming up, this may simmer for a while.
The 27-year-old forward - a Europa League victor with Atletico in 2017-18 after scoring 29 goals in all competitions - has a reported €100million release clause.