The then 18-year-old signed for Sir Alex Ferguson's side from Sporting Lisbon in 2003, but Wenger believes he was 'so close' to getting there before United.
Speaking to Arsenal's official smartphone sponsor, Huawei, Wenger said: 'My biggest regret, I was so close, to signing Cristiano Ronaldo, and not only did I not get him, he signed for Manchester United, so that of course still hurts today.'
Wenger also claimed that his greatest ever signing was Cameroon defender Lauren, rather than Gunners legend Thierry Henry.
He added: 'I’d never say which player was the best, but I think it’s the signings like Lauren who you spot when nobody else does.
'He was a right midfielder who I played at right back and was one of the Invincibles'
Having scored 15 goals in 15 games against Arsenal, Wenger unsurprisingly named Didier Drogba as a player he would have rather managed than played against.
Speaking of the Ivorian striker, now back with Chelsea, the Frenchman said: 'I missed him when he was playing in France and I knew he was a good player then.
'And he hurt us so much in big games, and so if he played for us it would not have happened'.
Without a win since the opening day of the Premier League season, Wenger's side face an in-form Aston Villa outfit on Saturday.
Despite sitting in seventh place, Wenger believes his side are in a 'comfortable position' to challenge for the title.
He added: 'We’re in a more comfortable position; we can keep our big players and buy big players such as Mesut Ozil and Alexis Sanchez.'