Barcelona have already spent in excess of £350million since last summer on forwards alone following the arrivals of Ousmane Dembele and most recently Philippe Coutinho, including Messi’s signing on fee for his new contract.
But they are reportedly still interested in bringing in another striker to bolster their options.
And Griezmann is believed to be the favourite among club chiefs with Atletico Madrid prepared to listen to offers at the end of the season.
The France international was heavily linked with a move to Manchester United last season but Atletico’s transfer ban led to him committing to the La Liga side for at least one more season.
And despite spending £142m in signing Coutinho this month, Barcelona will now switch their attention to making another big move for Griezmann.
However, according to Spanish outlet Mi Otra Liga, Messi has warned the Catalan club against a move for Griezmann.
He has instead told Barcelona to focus their efforts on prying Dybala away from Juventus.
Reports last month suggested clubs would have to stump up £140m in order for the Serie A giants to consider selling their prized asset.
Dybala has been one of Europe’s leading goalscorer for the past few years and has continued his fine form this season with 17 goals in 28 games.
But Barcelona’s interest in signing the 24-year-old may have taken a hit following his comments about the prospect of playing alongside Messi back in October.
“It is not easy to play with Messi because we play the same way,” he said.
Despite Dybala’s talents, he has only recently staked his claim with the national team, edging out Gonzalo Higuain in the starting line-up.