PSG had discussed a bid for Di Maria, whom Spanish media have reported has a price tag of around 75 million euros (59.58 million pounds), with European champions Real, PSG president Nasser Al-Khelaifi told reporters at the presentation of new signing David Luiz, according to French media.
"But it was too expensive and we ended the talks," he added.
Di Maria, who shone for Argentina at the World Cup before picking up an injury in the last-eight game against Belgium that ruled him out of the semi-final and final, returned to training with Real on Tuesday.
The club have not officially confirmed they are looking to sell the player and coach Carlo Ancelotti has said he is counting on the 26-year-old for the coming season.
Di Maria joined Real from Benfica in 2010 and was a key performer last term when the club won a record-extending 10th European crown and the King's Cup.
He was voted man of the match in the Champions League final against Atletico Madrid.
(Writing by Iain Rogers, editing by Justin Palmer)
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