The 29-year-old ended up staying in France, but he has admitted a transfer to Barcelona almost happened.
"Being around at the same time as Messi has made it much more hard for him", Di Maria told TyC's Libero show, as cited by AS.
Part of the temptation of Barcelona was the chance to play with Lionel Messi, as Di Maria explained.
"Lionel Messi? He's the best every year, it's always the same".
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"I started 2018 on a good foot, though, and I am really happy. Cristiano Ronaldo's a special player, but Messi's from another planet", he said.
The Catalan giants made one of the most memorable comebacks in football history when they overturned a 4-0 first-leg defeat to Paris-Saint Germain last term, but they would exit the competition the very next round after to failing to score against Juventus in two games.
"Without Neymar we are more balanced", Messi told The Mirror.
But Messi does not think Madrid - lagging 16 points behind Barca in LaLiga - will challenge due to their surprisingly poor form this season.