Zungu, who was also wanted by SuperSport United, is expected to sign with the Brazilians on Monday pending the results of his medical.
Downs have already signed a number of new players, including Kennedy Mweene, Raymond Monama, Tiyani Mabunda and Rodney Ramagalela.
AmaTuks are expected to receive R3-million plus “a few players” – including Siyabonga Ngubane – in exchange for Zungu.