The Brazil international admitted he almost joined the Blancos in 2008 and backed former manager Pep Guardiola to succeed at Manchester City
Alves signed for the La Liga champions in 2008 for a then-record fee for a full-back when Barcelona paid Sevilla €30million.
But Alves said his fate might have been different had he seen through a move to Real Madrid which he says was almost done.
The revelation came during a Spanish radio interview in which Alves discussed Neymar's future at the club.
"People should know Neymar and his family better before they give their opinion," Alves told Spanish radio station Onda Cero.
"In life, people move on their interests and even more when money is an issue.
"I never hid my move to Real Madrid was almost done ... my fate changed and I arrived at Barcelona instead."
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In his first season at the Camp Nou, Alves won a remarkable treble of trophies in Pep Guardiola's famous side which captured La Liga, Champions League and Copa del Rey triumphs during the 2008-09 campaign.
Since, he has won a further four league titles, two Champions Leagues and two Copa del Rey winners' medals.
A central figure in those successes was Guardiola, and Alves believes the Spaniard was attracted to Manchester City because of the size of the project.
"Barcelona happened to be a reference when the collective worked and individuals made the difference ... Pep Guardiola rescued that and now we have developed the idea," he said.
"Pep will be whatever he wants to be. He is able to re-make himself, has dedication, study... he has a gift to manage.
"I think he did not like Bayern [Munich] because he wants a revolution from the very beginning ... he will do that at Man City.
"Let the rest prepare for that."