The Red Devils completed a deal for the now Real Madrid attacker back in 2003 when he was just a teenager at Sporting Lisbon.
However, Wenger has claimed that but for the intervention of former United coach Carlos Queiroz, the Portugal captain could have worn the number nine shirt at the Emirates Stadium.
"He was very close to coming here. He has a number nine shirt with Ronaldo on the back from Arsenal Football Club," he told ITV Sport.
"What happened was that Carlos Queiroz went to Manchester United and they snapped him away from us because he knew him from Sporting. That's what life is about. You give your best but sometimes you might find that people are stronger than you. That can happen as well."
United received £80m for the 28-year-old when he left for Madrid in 2009.
Ronaldo Footballing Superstar is on ITV 4 tonight at 10pm with interviews with Ronaldo, Wenger, Rio Ferdinand and more.