The Argentine arrived at Manchester United for a British transfer record, but Nasser Al-Khelaifi insists the winger was close to joining the Ligue 1 champions
The Argentina international had been the subject of speculation for weeks before sealing a move to Old Trafford for a British record fee of £59.7million last week.
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"For two or three weeks, I have discussed this issue with my friend Florentino Perez, president of Real Madrid," he told Le Parisien.
"We met twice, we made an offer, but we are not agreed on the price. For me it was too expensive. It has nothing to do with the financial fair play. The player wanted to come to Paris, but this was not possible."
Al-Khelaifi also revealed that Barcelona tabled a big-money bid for defender Marquinhos, but PSG had no intention of selling the Brazilian.
"We received a very large supply of FC Barcelona, more than €40 million [£32m]." he said.
"But we do not buy players for resale. We are not there to do business, we are here to build a great club with great talented players.
"If it was to do business, we would have sold three or four players this summer. It's not my philosophy.”
The PSG supremo also denied that Edinson Cavani was eager to leave Parc des Princes during the transfer window after several clubs were linked with the Uruguay striker.
Cavani has largely had to play second fiddle to Zlatan Ibrahimovic as PSG's main striker since his arrival, but Al-Khelaifi has backed the 27-year-old to channel any frustrations into positive performances.
"He is very happy in Paris, he loves the club, he is fully in the project," said Al-Khelaifi
"When he misses a game, he's angry, it's normal, he's a competitor. After, I can confirm that many clubs wanted [to sign Cavani]. And I can confirm that many great players want to come to Paris."