As a World Cup winner, a prolific presence had found himself registering on the radar of those in Catalunya for some time.
Griezmann spent several months weighing up his options, before airing his intention to remain in the Spanish capital during an infamous video reveal.
Talk of Barca retaining an interest in the 28-year-old has rumbled on from that point, with another approach mooted for 2019, but Laporta believes a loyal fan base have moved on.
Quizzed on the renewed links to Griezmann, Laporta – who acted as Blaugrana president between 2003 and 2010 – said at the World Soccer Congress: "They will decide what they think is best, but I think that most of the fans don't want him.
"This is mostly because of the price being quoted, I think it's inflated, there are other players with great potential who can play Griezmann's position.
"People have to want to come to Barcelona, he's a great player but he had the opportunity last year and didn't take advantage of it, he played games with Barcelona."
While Griezmann may be set to remain at Atletico in the next transfer window, plenty of movement is expected at their cross-city rivals Real Madrid.
Laporta admits to having taken pleasure in seeing the Blancos struggle this season, with a turbulent campaign having delivered three managerial changes and no silverware.
He added on goings on at the Santiago Bernabeu: "I think the answer is obvious, Real Madrid's season has been a disaster.
"Being a Real Madrid fan must be difficult at this moment because you can't win anything and you have to start to think about the summer.
"It's very hard, I don't want to disrespect anyone because it's a very sensitive subject, but it's a pleasure for Barcelona people when things are bad for them, and vice versa."