The Swedish international has never fully committed his future to the Milanese giants and Laporta is attempting to prise the former Juventus star to his treble winning side.
After negotiations for Valencia hitman David Villa reportedly broke down, the Blaugrana patron claimed the club would be exploring other options and it seems one of them could be 'Ibracadabra'.
Earlier in the summer, reports also emerged that a swap deal between the two clubs that would see the ex-Ajax player move to the Catalan club and Samuel Eto'o move in the opposite direction was in place, but the transfer never materialised.
The two club's have been involved in a fair bit of activity with one another lately, as Barcelona have already confirmed they will be signing Inter left-back Maxwell for approximately €5 million and on Thursday stories emerged that the Serie A outfit were on the verge of taking Aliaksandr Hleb on-loan.
UPDATE: 00:30 CET: Inter president Massimo Moratti has admitted that he has met with Laporta to talk about a swap deal involving Ibrahimovic and Samuel Eto'o.
"I have met Laporta. We spoke about Eto'o and Ibrahimovic," the oil tycoon stated.
Sky Sport Italia are claiming that Inter could sell Ibrahimovic to Barcelona for 40 million euros, plus Eto'o and Hleb.
Could this be Inter 2009-10?
Adam Scime, Goal.com