Laporta, reports Sport, is keen to bring Aguero back to Spain this summer.
However, any deal with Barca will involve Aguero accepting a cut on his current €12m-a-year wages. The striker's deal with City expires in June.
Meanwhile, local reporter Jose Alvarez said on El Chiringuito this week: "Aguero has an offer of two years from Juventus.
"But he wants to play with (Lionel) Messi in Barcelona."