Messi has a contract with Barcelona until June 2018 and seems unlikely to leave the Camp Nou side anytime soon at this stage, but Di Maria refuses to rule out a reunion with his compatriot at the Parc des Princes.
"I hope that PSG can bring Messi to Paris one day," Di Maria told RMC .
"Everything is possible. It is all about money. It would take a lot of money to sign a player like him.
"It would be great for Ligue 1 and French football in general if Messi joined PSG.
"PSG have the resources to sign him. Messi could come to Paris."
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Messi enjoyed a fine 2015 as he guided Barcelona to the treble and Di Maria has backed his compatriot to win the Ballon d'Or ahead of Cristiano Ronaldo and Neymar.
"Messi, Ronaldo and Neymar all scored a lot of goals and had spectacular years," Di Maria added.
"But the Champions League often plays a big role in who wins it and Barcelona won that competition. That's why I think Messi has the best chance. He won the treble and has a good chance.
"Ronaldo also had a good season, but is not the favourite like before."