World Cup winner Griezmann has been a vital part of Diego Simeone's squad over the last five years, winning three major titles including the Europa League.
The 28-year-old has also been Atletico's top scorer in each of the last five seasons while finishing third in the voting for the Ballon d'Or on two separate occasions.
Griezmann came close to a switch to Barcelona last summer before ultimately signing a new contract at Wanda Metropolitano, but one year later he has announced his intention to leave the club.
The France international released a video on Atletico's official website on Tuesday revealing his desire to move on to a new challenge, which has fueled plenty of transfer speculation.
Barcelona are thought to be leading the race for his signature once again and Valverde has confirmed an official approach has already been made.
Speaking after watching his side draw 2-2 at Eibar on the final day of the Liga season, he said: “It is true we have already made contacts.
"It is true that contacts are ongoing, but the season isn’t over yet. We have the Copa Del Rey final still to play.
"We have the chance of winning two titles and we must try to focus on this issue
“Afterwards we will have time for everything else – we won’t say anything new when we are talking about players from other teams.
“We will see. He [Griezmann] is a great player. We’ve always said so."
Barca secured a second successive title back in April, having led the table ahead of rivals Atletico and Real Madrid for the majority of the campaign.
Griezmann, meanwhile, said his final goodbyes as Atletico drew 2-2 with Levante on Saturday, ending the season in second place behind Barca.