The France international is available for €100 million (£88m) due to a release clause in his deal with Atletico, and Barcelona are at the front of the queue to sign the striker.
Reports have suggested that Griezmann is ready to reject the chance to join Barcelona and sign a lucrative new contract with Diego Simeones side.
But Messi is keen to play alongside the 27-year-old at Camp Nou.
Hes a great player and we would understand each other, Messi told Mundo Deportivo.
Hes going through an exceptional moment in his career.
Its not yet one hundred percent, but the more quality we have, the better.
We want to be the best team in the world, and for that we have to look at the best.
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