Speaking over the weekend, Barca president Josep Maria Bartomeu revealed he had met with the player's agent and also held unspecified talks with Atleti president Enrique Cerezo.
The 27-year-old has long been linked with a move to the Liga champions and is expected to clarify his future prior to the World Cup.
"I don't know how relevant it is that Bartomeu spoke with the Atleti president," the Barca boss said.
"He's a great player, I have no doubt about that. I'm sorry but I think we have to be cautious about players who don't play for us.
"I think we have to respect what we have here and also our opponents.
"Griezmann has a final coming up and we have to be careful. He's a great player, that's clear. In the future, we'll see what happens."
Barca host Villarreal on Wednesday, three days on from a 2-2 draw with Real Madrid, in which Sergio Ramos criticised Lionel Messi for allegedly attempting to influence the officials.
Madrid defender Ramos said Messi was wrong to speak with referee Alejandro Hernandez Hernandez in the Camp Nou tunnel at half-time, but Valverde countered that suggestion by claiming it was commonplace.
"Situations come up all the time. I think players speak to referees and referees speak to players," he said.
"I have a lot of experience, I have seen many things from many teams, and in the tunnels as well. Nobody [is alone] in that sense, I guarantee it."