Wenger says former chief David Dein had come close to signing Ronaldo before United came in, but Arsenal eventually balked at the price Sir Alex Ferguson was willing to play.
The departing coach feels Ronaldo's impact would have "changed history" at Arsenal as the club were unable to match United's trophy haul during the Portuguese's rise to prominence.
"The obvious player [that we missed out on] that comes to mind is [Cristiano] Ronaldo," Wenger told Arsenal.com.
"He was here with his mother and we were very close. Then Man United came in and they had Carlos Queiroz at the time, who was their coach. United played against Sporting Lisbon and Ronaldo was outstanding and they signed him.
"You could imagine at the time what it would have been like to have Thierry Henry and Ronaldo together. Later Man United had Rooney, Ronaldo and Van Nistelrooy together, they had an exceptional football team, and Giggs and Scholes together. That would certainly have changed a little bit the history of my stay here as well."
He added: "There is always something you could have done differently, but the problem of negotiations is to know when you give in and when you don’t give in," said Wenger.
"Once we were at £4.5 million, we were still in negotiations. David met with [Ronaldo’s agent Jorge] Mendes in Paris and he was representing Sporting, so we were very close. But Man United went to £12 million, which we could not afford at the time."