The Arsenal captain was part of the academy structure at Camp Nou before being lured away to London in 2003.
His impressive development has seen Barca attempt to bring him back to his Catalan roots on numerous occasions, with Fabregas admitting that he would welcome such a move at some stage in his career.
Laporta, who failed to land Fabregas during his reign as president, hopes a deal can be done, and with it make a point to the Premier League who poach Spanish talent.
"The English come here to do 'fishing'. They came to fish for Gerard Pique and they came to fish for Cesc. It is an issue of justice that we now want to recover them," said Laporta.
"I would have liked it if Cesc came to Barca in the way that Pique came. He abandoned Manchester United, making it clear he was going to Barca. They were players who were formed here."
Laporta doubts whether Fabregas will be back at Camp Nou this summer, but it is only a matter of time.
"What happened at that time was that we wanted to make the investment in Villa before the World Cup," Laporta said on Barca's failed attempts to land the Spain international in 2010.
"We had tried the previous year and could not sign him because Valencia asked a lot of money.
"Cesc is a great player and I would like him to come back. But his signing is not urgent while we have Xavi, [Andres] Iniesta, [Sergio] Busquets and [Seydou] Keita. I think next season or the one after he could come here."