Italy international Verratti, who has previously been linked with a switch to Juve, has told PSG of his desire to leave the club this close-season, with Barca set to make a €100 million bid.
Reports in Catalonia suggest Barca director Javier Bordas met the 24-year-old and his agent Donato Di Campli while on holiday in Ibiza.
But Juve boss Allegri thinks Verratti, who was pictured at the same restaurant in Ibiza as Barca star Lionel Messi this week, will ultimately remain at PSG.
"He is a great player," Allegri said to Corriere dello Sport. "He is a PSG player, though, and I think he will stay in Paris."
Di Campli said last week that Allegri's men could be an option for Verratti, who joined PSG from Pescara in 2012 and has gone on to win four Ligue 1 titles in his first five seasons, although Champions League success has eluded him.
"It is not done!" said the Juve boss. "When I am back, Juve will have signed players to improve the team.
"Juve are at such a high level now that there aren't many champions on that level.
"To move forward we have to find those players who will complete us in the areas where we are weakest."