Di Maria was targeted in what Argentine authorities have previously described as an attempted display of power by criminal organizations in Rosario, which has seen an increase in drug and gang related violence.
The winger, who retired from international football after winning his second Copa America trophy earlier this month, said he had wanted to end his club career in his hometown after leaving Portuguese side Benfica.
Reports of a death threat note thrown into Di Maria's family property surfaced in March and Di Maria said his family had not reported another threat to the police out of fear.
"There was a threat at my sister's business, a box with a pig's head and a bullet in the forehead, and a note that said that if I returned to (Rosario) Central, the next head was that of my daughter Pia," Di Maria told a television station in Rosario on Tuesday.
"Those months were horrible... we could only sit there and cry each night over not being able to carry out that dream return."
Argentina captain Lionel Messi was also a target of threats last year. Argentina’s federal security forces were deployed to Rosario in March and Governor Maximiliano Pullaro said earlier this month that protocols were implemented to ensure the safety of public figures.
"It is disrespectful to talk about security and protocols for me when people from Rosario cannot go out to work, cannot wait for the bus without being robbed or killed for a backpack," Di Maria added.