Former United chairman Martin Edwards revealed in his new autobiography that the club sounded out Wenger after Ferguson announced he would retire at the end of the 2001-02 season.
But Ferguson changed his mind, eventually remaining in position until 2013, and Wenger says he has no regrets about staying put at Arsenal.
Asked if he had been tempted by United’s offer, the Frenchman replied: “No, because I was always happy here. More than people were happy with me, I was always happy here.
“I am always very confidential. Maybe one day I will get all the contacts I had during my stay at Arsenal and it will make a few chapters, but you should ask Martin Edwards.”
Writing in his autobiography, “Red Glory: Manchester United and Me”, Edwards said Wenger had shown enough interest in the role to meet him and chief executive Peter Kenyon.
“Our first choice was Arsene,” said Edwards, who was United’s chairman between 1980 and 2002.
“We thought he was the best candidate to replace Alex. Certainly he was my number-one choice.
“So we made our approach and Wenger did show a little bit of interest, enough to want to meet Peter Kenyon and me at his house in London to listen to what we had to say.”
Speaking after his side’s 3-0 win over Bournemouth on Saturday, Wenger said he had turned United down because he felt wedded to Arsenal’s values.
“Because I love the values of this club,” the 67-year-old explained, in comments published by British newspapers on Monday.
“For me, a club is about values first and as well because I know what has changed. One day it would be a good chat to have with the press to look at the evolution.
“A lot has changed, but when I came here this club was about values that I love in sport and that’s why I’m still in the competition.
“So I will always question myself. Yes, of course Man United is attractive, but am I happy here? The answer is yes.”