Manchester United was close to reaching an agreement to sign the winger this summer but could miss out to Paris Saint-Germain, who have now emerged as frontrunners.
Caballero, who recently completed a move from Malaga to the Premier League champions, says his countryman would do well in England.
"[Di Maria's] way of playing and his pace would make him a success," he told Goal. "He'd shine. I think some people doubted him when he moved to Spain but he has been excellent.
"He shut the mouths of many journalists in Spain who doubted his talents. I think he would shine in any league."
Caballero also said he is looking forward to playing in the Premier League, which he feels will be a step up from his previous stops.
"I think it's a great league – a fabulous league," he said. "On a personal level, it will be a big change, like when I moved up from the second division to the first [in Spain].
"The demands are great. Lots of teammates, like Roque Santa Cruz, spoke very highly of the Premier League. They told me it was the best, that it's fantastic. Now I have the chance to experience it first-hand, and I hope I'm up to the task."