Messi has enjoyed astonishing success with Barca and developed into arguably the world's best player, winning the Ballon d'Or a record five times.
The Argentina star has also won eight LaLiga titles and four UEFA Champions Leagues, but it all could have been so different.
Laporta, who was Barca president from 2003-2010, revealed Inter met Messi's buyout clause more than 10 years ago.
"It was 2006 when Inter made an offer," he told The Guardian.
"They were prepared to pay the €150 million ($220 million AUD) buyout clause, which is why we [later] raised it to €250m ($367m), but I always felt reassured by my relationship with his dad, Jorge.
"I told him: 'They'll have to pay the clause because I won't sell. He'll be happy here, he'll get glory. There, he'll only win financially. Your son's destined to be the greatest in history and here he'll have a team to help get there. He'll enjoy it.'"
Messi remained at Barca, dominating in Spain and Europe to be in the discussion over the greatest players of all time.
Laporta believes the 29-year-old is the best ever, describing him as a mix of Johan Cruyff and Diego Maradona.
"I'm very Cruyffista, but what Leo does – and I talked about this a lot with Johan – makes him the best in history. Johan said so too," Laporta said.
"Messi's football is beautiful and effective. For me the best ever are Cruyff, Maradona and Messi.
"Leo's a mix of Cruyff and Maradona but he is Leo Messi."