The experienced attacker spoke highly about Latin American football but stressed he has not spoken with Trezeguet about moving to the Buenos Aires-based club
The 37-year-old is looking for the next challenge of his career as he enters the final weeks of his contract with Juventus, who decided not to offer the striker an extension.
Swiss side Sion and Major League Soccer (MLS) club Montreal Impact have both expressed their interests in Del Piero, who has not yet given any indication of a preferred destination.
Questioned about the possibility of signing for River Plate, who are currently in the Argentine second division, the former Italy international does not exclude the possibility of reuniting with David Trezeguet, whom he played alongside at the Bianconeri between 2000 and 2010.
"My future? This is a delicate moment for me," Del Piero told ESPN. "I do not know what I will do, where I will go. We will consider every offer that arrives.
"Have I spoken about River with [David] Trezeguet? Honestly, no. We have not talked about that.
"Perhaps someone will call me, I do not know. Latin football is also my football."
Del Piero then relived the winning goal he scored in Juventus' 1-0 victory against River Plate in the 1996 Intercontinental Cup in Tokyo.
"We had a hard time in that match and before our goal, Ariel Ortega hit the bar and then Angelo Peruzzi made a fantastic save," he said.
"We were the two best teams in the world and, as it always happens in such even matches, everything was decided in one play.
"I have travelled a lot in my career, and Boca Juniors' fans have always come to me and greeted me for that goal against River.
"I have always regarded them as two great teams."
River are currently second in the Nacional B, two points behind leaders Rosario Central, and are on course for atomatic promotion to the Argentine top flight.