There were suggestions that the La Liga leaders made an approach for Griezmann in January transfer window.
However, they were forced to deny those claims in an official statement after Atletico Madrid reported them to FIFA.
Barcelona had already spent £142million on Liverpool’s Philippe Coutinho last month but still wanted to add another striker to their ranks.
And Sky Sports journalist Guillem Balague believes that Griezmann will move to the Nou Camp in the summer for around €100million (£88.2m).
“Griezmann is definitely a target – €100m (£88.2m) is what he will cost this summer,” Balague told Sky Sports.
“Barcelona feels that Griezmann has been very positive about the possibility of joining Barcelona as well.
“Even though Atletico has taken the case to FIFA, for the alleged illegal approach of Barcelona, basically what Atletico have told Griezmann is, ‘If you want to stay, we’re happy for you to stay, if you want to go, there are other ways of doing this’, so they are just being realistic to Griezmann.
“Atletico wanted to take pressure away from him and focus on the rest of the season.
“To be honest, in the last month, Griezmann has been a better player.
“With Diego Costa next to him, you’ve seen a player that has delivered much better than he had done earlier in the season, scoring a goal or an assist in six of the last seven games.
“Of course he’s absolutely a target for Barcelona, no doubt about it.”