The future of France international Griezmann - who signed a new five-year deal in June - was the subject of widespread speculation following an impressive Euro 2016 campaign in which he inspired his nation to the final.
Late last month, Cavani sparked rumours of a possible union when he posted on Twitter to invite Griezmann to join him in enjoying some mate, a traditional drink in Cavani's native Uruguay.
Cavani said the media had got carried away with the situation but did express his desire to one day count Griezmann as a team-mate.
"It's the press that said I wanted to invite Antoine Griezmann to Paris," he said.
"I sent him a message to take a Uruguay mate. I'd like to play with him one day, he is a great striker and a beautiful person too."