Messi's future at Barcelona remains unclear with just under six months remaining on his current deal.
PSG have already confirmed their interest in the six-time Ballon d'Or winner, which could change Di Maria's mind about staying at the club as his contract comes to an end this year.
"I had the opportunity at one moment in my career to go to Barcelona but it was not done," the Argentine told TyC Sports.
"We could say that there is another chance to be able to play with him but my contract is coming to an end and I do not know what will happen. But I would be very happy to play alongside him.
"I have already played with Cristiano Ronaldo, Neymar, Kylian Mbappe. If I could play as well with Leo, I could happily retire after that!"
"My wife told me, 'if Leo comes, we will at least stay and you will make him a barbecue'.
"It would be the best. I could not ask for anything more in football."