Germany's top-selling daily Bild reports that Dortmund's chief scout and a lawyer are in Argentina to finalise details with the 19-year-old Boca Juniors defender, who will be offered a contract until June 2023.
The clubs have agreed a transfer fee and the centre-back is expected to arrive in Dortmund at the end of next week for a medical.
Dortmund's CEO Hans-Joachim Watzke has said the German league leaders want to strengthen their defence to cover for Swiss centre back Manuel Akanji, who is sidelined long-term by injury, with the current transfer window to close in Germany at 1700 GMT on January 31.
Dortmund's scouting department is currently busy as they look to invest the £58 million ($74m) made from selling US international Christian Pulisic -- regarded as one of the hottest properties in European football -- to Chelsea at the start of January.
Borussia Moenchengladbach's Belgium winger Thorgan Hazard, 25, is also believed to be a target as he has yet to sign a contract extension to his current Gladbach deal which expires in 2020 and would reportedly cost Dortmund 42 million euros.
The Bundesliga resumes the weekend after next with Dortmund, who hold a six-point lead in the table, travelling to fourth-placed RB Leipzig on January 19.