Van Persie was public enemy number one among the Arsenal fan base after his hugely successful eight-year spell at the club came to an acrimonious end in the summer of 2012 after joining Manchester United.
He played a starring role in his first season at Old Trafford under Sir Alex Ferguson's tutelage as United won a 13th Premier League title.
But following Ferguson's retirement, two years later Van Persie was a peripheral figure at the club and looking for a transfer.
It was then that Van Persie picked up the phone and called his former boss about the possibility of returning to the Emirates, but he was unable to grant his request.
"In 2012, he announced his intention not to extend his contract," says Wenger in his new book 'Arsene Wenger: My Life in Red and White'.
"All the big clubs were courting him. I sold him to Manchester United.
"The supporters were angry with me for this but we could not match the offer. I managed to negotiate his departure for £24million, which was a huge amount at the time for a player with a year left on his contract."
He continued: "I had only the interest of the club in mind. My relationship with Alex Ferguson and Manchester United had improved by then, but every transfer is a polite game of poker where you attempt to give not anything away.
"Van Persie had a fantastic first six months at Old Trafford: he put the team on track for the Premiership title and made it even more difficult for us.
"But after three years of the four that he signed for, he was injured and (Louis) Van Gaal sold him to the Turkish club Fenerbahce.
"He called me because he wanted to come back, but it was impossible: he was at the end of his career and we were investing in young players."
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Arsene Wenger has revealed that Robin van Persie personally contacted him in a bid to secure a return to Arsenal in 2015, but he turned the Dutchman down.