Off contract in June, Aguero will leave City this summer after ten years with the club.
A Bosman move to Barca has long been suggested and El Chiringuito's Jose Alvarez reports Laporta is about to complete an agreement with Aguero. The operation is expected to be closed in the coming days.
It remains to be seen whether this will be enough to retain Lionel Messi, who would have demanded the arrival of his compatriot and close friend.
Like Aguero, Messi also comes off contract at Barca next month.