The Real Madrid winger, who scored the extra-time winner in a 1-0 victory over Switzerland in the second round, limped out of his country's quarter-final against Belgium with a thigh complaint.
Di Maria subsequently missed Wednesday's semi-final, with Enzo Perez starting in his place, and remains a doubt for the clash with Germany at the Maracana.
"Angel is at a stage of recovery and there cannot be a time frame put on it," his agent, Eugenio Lopez, told radio station FM Delta.
"He was subjected to treatment with stem cells to accelerate recovery.
"Angel wants to play, no matter what, and he will make every effort to get there.
"Whether Angel will play will depend on the decision taken by [coach Alejandro] Sabella."Argentina booked their first World Cup final in 24 years with a penalty-shootout victory over Netherlands on Wednesday.