Wenger says Van Persie contacted him to try and arrange a return to Arsenal in 2015, but he decided to turn the Dutchman down.
Van Persie had sparked fury among the Gunners fans by joining Manchester United in the summer of 2012 after scoring 132 goals in 278 games for the north London club.
"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. I had only the interest of the club in mind.
"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 Ferguson [note: it was actually 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."