Wenger said: "Ronaldo is a great player and yes, we had him here and were very close to signing him, he could tell you this if he wants.
"But Manchester United had the partnership with Sporting Lisbon back then because Carlos Queiroz came in and tied up that link.
"That was the difference. One day, I will tell you more about the story and I am sure you will all be very surprised."
Wenger gave Ronaldo a tour of Arsenal's training ground at London Colney - but the Portuguese star opted to join Queiroz and Alex Ferguson at Old Trafford.
United signed Ronaldo, who is 23 on Tuesday, for £12.25million from Sporting Lisbon in 2003.