Reports have suggested that Griezmann is ready to reject the chance to join Barcelona and sign a lucrative new contract with Diego Simeone's side. "United have a very good relationship with Dortmund, the teams were talking more closely [but] he chose to go to Arsenal instead".
Following last year's strong links with Manchester United that culminated in the French global extending his contract with Los Rojiblancos - then under a recruitment ban - until 2022, Griezmann, who has a release clause of €100million (£88m), finds himself at the centre of a drawn-out transfer saga for the second successive summer.
Messi, who is preparing for Argentina's opening World Cup game against Iceland on June 16, also believes that Griezmann would be an ideal signing.
"He's a great player and we would understand each other", Messi explained to Mundo Deportivo.
"He's going through an exceptional moment in his career".
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Griezmann's performances this past season were eye catching as well, despite talks of him not being in the right state of mind after his move to Manchester United fell through last 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.
As Antoine Griezmann considers his future, the FC crew discuss the pros and cons of staying at Atletico and moving to Barcelona.
Messi, who has previously said he would welcome Griezmann at the Camp Nou, has again insisted the 27-year-old is one of the best in the business and that he would suit the Catalans.