Messi, 33, left Newell's for Barcelona in 2001 and has developed into one of the best players of all-time, winning a record six Ballons d'Or.
The Argentina captain has spoken about potentially returning to Newell's previously and D'Amico is hopeful, with the club having seen Diego Maradona arrive in 1993 after he starred in Europe.
"I don't know if it's impossible," he told TNT Sports.
"It's a decision exclusively made by him and his family. We have to have the best possible context to help make a decision.
"When Maradona came to Newell's, nobody thought that he would come either. I hope to do something similar with Leo."
Messi is contracted at Camp Nou until next year, although will reportedly extend that deal until 2023.
D'Amico is staying calm about the star's potential return to Newell's, saying: "Obviously, that's not to be selling smoke.
"It's a difficult topic. What Newell's fan would not dream to see the best player in the world with the jersey of their team on? Time might allow such things, you have to be calm."