Atletico midfielder Koke said on Thursday his team-mate was happy at the club but indicated he should move on if he no longer feels completely committed.
Valverde insists the talk is simply a rumour at present, much like suggestions of Real Madrid's interest in Neymar, but stopped short of ruling out a bid in future.
Asked whether Griezmann to Barcelona or Neymar to Madrid were the most likely, he told a news conference: "Neither. Rumours are rumours."
He then continued on Griezmann: "He is a great player and every time players are linked with Barcelona, they are great players.
"But I'm happy with the ones I have and, in the future, we'll see."
All back together at last in training! pic.twitter.com/rcVG2hjJJC— FC Barcelona (@FCBarcelona) November 16, 2017
Valverde would also not confirm whether Denis Suarez will stay at Barca beyond the next transfer window.
The midfielder has been linked with the likes of Napoli, having only made two starts in the league this season.
Valverde says Suarez remains in his plans but is not ruling out business of any kind in January.
The coach explained: "He is one more player in the squad. It's true he's played in some games and not others but I'm counting on him for the matches. It then depends on his form and the circumstances.
"He's fine. I can't comment on one newspaper story or another.
"The club is open to all kinds of possibilities. Not only Barca – any club. We value what we have but we are not going to close doors."
However, Valverde suggested they would not look to sign another centre-back despite Javier Mascherano having been ruled out for a month with a hamstring injury.
"You can never predict injuries," he said. "We have four good centre-backs. We trust everyone: [Gerard] Pique, [Samuel] Umtiti and, of course, [Thomas] Vermaelen. We have the B team, too."