Sporting director Nicolas Burdisso spoke last month of his desire to see De Rossi join Boca after the World Cup winner left boyhood club Roma.
And despite reports the Italian would instead retire, links to the Argentine giants have persisted.
Angelici now hopes a move is close, claiming negotiations are 99 per cent of the way.
"The negotiations for De Rossi are well under way," he told TyC Sports. "In the coming days, he will fly to Buenos Aires.
"It is 99 per cent that Daniele will be a Boca player.
"To have a world champion say he wants to finish his career here fills me with pride. It is good for Argentine football to have a player like this."
De Rossi would likely replace Uruguay star Nahitan Nandez, who is a reported target for Cagliari.