The five-time Ballon dOr winner, who has gone on to win the Champions League four times, left Portuguese side Sporting in 2003 to move to Old Trafford, where he emerged as one of the greatest players in the world.
But it could have been different had Arsenal wrapped up a deal for Ronaldo quicker, with Wenger revealing that the club took too long to negotiate a deal.
Asked to name the biggest player he almost signed, Wenger told Arsenals website: The first very obvious one that comes to my mind is Ronaldo.
He was here with his mother, we were very close, and then Man United came in because they had Carlos Queiroz at the time – they took him on as a coach. And they played against Sporting and Ronaldo was outstanding and they signed him.
So you could imagine at the time to have Thierry Henry and Ronaldo together, like then later United had Ronaldo, Rooney, Van Nistelrooy all together.
They had an exceptional football team with Giggs and Scholes together. That certainly would have changed a little bit the history of our football club and my stay here as well.
On how United hijacked the deal, Wenger continued: There is always something you could have done differently.
The problem with a negotiation is always to know when you give in and when you dont give in. And once we were at £4.5m we wanted maybe still negotiations, I dont exactly remember.
But with David [Dein] we met [Ronaldos agent Jorge] Mendes in Paris and he was representing Sporting. So we were very, very close. But Man United after they went to £11m or £12m which at the time we could not afford.
United spent £12m on Ronaldo back in 2003, and six years later he became the most expensive player in the history of football when he joined Real Madrid for £80m.
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