Griezmann has reportedly been a top target for Barca in recent years but the Catalan giant has thus far been unable to tempt the France international to make the switch to Camp Nou.
At the end of the 2017-2018 season Griezmann featured in a television documentary, made by a company owned by Barca defender Pique, in which he mulled over his future before announcing his decision to stay at Atletico.
But reports in Spain this week have suggested Griezmann is unsettled at Atletico and wants to join Barca to boost his chances of winning more major titles to add to the World Cup glory he enjoyed with France.
"If he wants to come, you have to ask him," Pique told reporters after a 4-1 win at Real Betis moved Ernesto Valverde's side 10 points clear of Atleti at the top of the LaLiga table.
"Another documentary? Not for the moment. And if there was, I would not tell you."
Lionel Messi, just four days on from scoring and assisting twice in a 5-1 hammering of Lyon to reach the Champions League quarter-finals, was again in top form against Betis.
The Barca captain scored a hat-trick, which was completed by a stunning lob that clipped the crossbar after looping over goalkeeper Pau Lopez, leading to a stirring ovation from the home fans.
Barca next faces Manchester United in the Champions League but Pique noted that even with Messi at his best it cannot assume it will progress to the last four.
"He's a special footballer," Pique said. "There have been others in history, but Leo has been doing it for 14 years, and he's unique in that there's no one like him.
"These are three very important points and the difference is also very important, but there is still a lot to play for, the sensations are good, but you have to go step by step.
"It's good that people are excited, but with their feet on the ground, LaLiga is closer, but the Champions League has shown us that in the quarters things are complicated for us."
Barca has been knocked out in the quarter-finals of the Champions League three years in a row, including a collapse against Roma in last season's competition having taken a 4-1 first-leg lead.