The 17-year-old midfielder, also called Diego Maradona, is currently at his father's former club Napoli in Italy's Serie B.
He has met his father only a few times after his Italian mother fought a legal battle to prove her son's paternity.
"I've got a contact in Napoli and we've heard he's a good player so he's coming over," Blackburn manager Graeme Souness told the BBC.
"You can imagine the ridiculous pressure he is under over there and he fancies having a go somewhere else."
Maradona senior, 43, is regarded as one of the finest players in the history of the game. Four years ago he was voted "player of the century" by fans on FIFA's official website.
He led Argentina to World Cup victory in 1986, when he scored one of the best goals in the tournament's history in the quarter-final against England, but has spent much of the past four years undergoing drugs rehabilitation treatment in Cuba.
His personal doctor recently said he had lost over 20 kilos (44 pounds) at a psychiatric clinic in Buenos Aires, where he was taken against his will by his family for cocaine addiction in May.
