Manchester City and Paris Saint-Germain have distanced themselves from the FIFA World Cup-winning forward, with Barcelona being linked as his most likely next destination.
Griezmann announced his decision to leave Atletico Madrid in a video posted on his social media accounts last week, thanking the club's supporters for "five incredible years".
He has been linked with a transfer to Camp Nou for more than a year, opting to sign a new five-year contract at the Wanda Metropolitano before the start of the 2018/2019 season rather than pursue a move at that time.
With the 28-year-old set to switch allegiances, and both City's Pep Guardiola and PSG's Thomas Tuchel saying they would not be signing him, Valverde was asked whether he would be looking to add Griezmann to his squad for next season.
"We always say the same — he's a player at a different club," Valverde said.
"Who knows? He's a great player, I've never denied that. Are you going to ask every coach in football if they want him? Is that your plan?"
When asked what role Griezmann might play in his Blaugrana team, Valverde responded: "If he came you would see.
"We're talking about an assumption, a player who might come, who could be here. I'm not going to talk about his position."
Barcelona clinched the LaLiga title with three games to spare and its clash with Eibar on Monday (AEST) is of relatively low significance to both sides.
But Valverde insisted he will name a strong side to ensure his players' match fitness does not wane ahead of the Copa del Rey final against Valencia six days later and deflected further questions about transfer targets, preferring to focus on his aim of winning the double.
Asked if he had new players in his sights, he replied: "I don't know, that's an internal club matter. There are other parties involved who might have an opinion.
"The club's idea is to make the best team we can, taking into account our strengths and weaknesses. Right now we've got a final to think about. We could win the double this year.
"It has been an extraordinary season — things were broken a lot by the way we went out of the [UEFA] Champions League, but we won the [UEFA] Super Cup, the league with three games in hand. We've got the cup final to come."
He added a word of reassurance over Lionel Messi, who was short of his best in Barcelona's 2-0 win over Getafe five days after its UEFA Champions League elimination at the hands of Liverpool, which overturned a 3-0 first leg deficit on a dramatic night at Anfield.
"When you lose a game the way we did [in Liverpool] that does hit you very hard," Valverde admitted.
"Leo [Messi] is fine, better every day. The days after going out of the Champions League you find it difficult – they are not a team that is used to losing.
"But they are looking forward to the cup final, Leo as much as anyone else."