The 22-year-old is one of the most coveted players in Europe after helping Juve win the domestic double and reach the Champions league final this season.
Laporta is hoping to return to Barca’s top post and is one of five candidates in the running to replace Josep Maria Bartomeu, who is standing for re-election.
“Pogba would be a great signing,” Laporta said to Spanish radio station Catalunya Radio. “He is a very strong player, very young and he is enthusiastic to arrive here.
“Everyone believes he would fit in Barca’s system.
“I have a good relationship with Pogba’s agent, Mino Raiola, since the time when we signed Maxwell and (Zlatan) Ibrahimovic.”
Reports in Spain claim Pogba, who is under contract with Juve until June 2019, is expected to remain in Turin for another season before the France international makes his move to the Nou Camp next summer.
Barca cannot field any new players until January 2016 due to a transfer ban imposed by FIFA for breaching rules on the transfer of players aged under 18.
Laporta, 52, previously served as president of Barca from 2003 until 2010.
Back in the 2003 elections Laporta, who did not start as favourite but won, promised to bring David Beckham to Barca.
Beckham would go on to join Real Madrid in a 35million euro transfer deal that summer from Manchester United.