Before linking up with Barcelona's youth team in 2001, Messi spent his earlier years at Newell's Old Boys, a club which has frequently been associated with a reunion with Messi during the latter stages of his career.
As it stands, the 33-year-old is expected to extend his stay at Camp Nou past the end of next season, but D'Amico has reiterated that the door remains open should the legendary attacker have a change of heart.
Speaking to TNT Sports, D'Amico said: "I don't know if it is impossible. It is all up to him and his family.
"As directors we have to provide the best context possible to help him make a decision. When [Diego] Maradona came to Newell's nobody thought he could come.
"I hope that something similar can happen with Leo. Obviously we shouldn't be making things up, this is a delicate subject. What Newell's doesn't dream of seeing the world's best player in their team's colours? Time will tell maybe, we have to stay calm."
While Barcelona are struggling to defend their La Liga crown, Messi has enjoyed another productive campaign, contributing 24 goals and 20 assists in Spain's top flight and the Champions League.