The Premier League club had hoped to agree a deal with Real Madrid, but the emergence of the Ligue 1 side could see the Old Trafford outfit outmuscled in transfer talks
The Old Trafford side had been confident of reaching an agreement with Real Madrid to sign the winger this summer as Louis van Gaal continues with a squad overhaul.
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And PSG president Nasser Al-Khelaifi has reportedly held talks in Madrid with the Spanish giants.
The offer of Champions League football from the French capital club is also understood to appeal to Di Maria, despite the presence of Van Gaal at Old Trafford.
United have pressed ahead with their summer transfer plans during the World Cup despite the Dutchman's continued involvement with the Netherlands in Brazil.
Ander Herrera was signed from Athletic Bilbao, while Southampton teenager Luke Shaw made a big-money move from Southampton.
But Van Gaal could miss out on another primary transfer target after Toni Kroos previously turned down the chance to leave Bayern Munich for the Premier League.
Di Maria, meanwhile, is facing a race against time to be fit for the World Cup final clash with Germany after picking up a thigh injury in training.