The Argentina attacker, 32, is coming off contract at the end of the season.
TyC Sports says Dybala is ready to leave Europe and return home this coming summer to join Boca.
Dybala's friend, Leandro Paredes, already plays for Boca Juniors - and the midfielder's father has said that he is interested in a move.
"I heard a conversation between Leandro and Paulo, and he said he would come. Paulo will play for Boca. His daughter will become a Boca fan and see her father play at La Bombonera," Daniel Paredes told Cadena Xeneize on November 11.
Already this summer, Dybala opened up about moving back to Argentina to play with Paredes.
"A return to Argentina? Yes, I have never played in the top division there and it is an option that I am considering. However, I do not know if it will happen. Leandro Paredes puts pressure on me every day to go to Boca Juniors with him, so yes, I am thinking about a return to Argentina.
"I am keeping the door open. It would have been enchanting. But right now I do not know," he said in an interview with journalist Gastón Edul in May.