The Daily Mail says Becks penned a two-year contract extension with the LA Galaxy in January, but it has now been revealed he was on the verge of jetting to Brazil for a season.
Botafogo landed their top transfer target Clarence Seedorf, but were also negotiating the signature of the former England international.
"When the negotiation was about to close, I spoke with the president - he and I have a pretty cool relationship," Carlos Alberto told ESPN Brasil.
"I was in Amsterdam in May and an influential businessman, a famous player, came to me at the hotel, saying there was a player interested in playing for a year in Brazil: David Beckham.
"If it did not work with Seedorf, he had this player to come to Brazil."
Botafogo president Mauricio Assumpcao later confirmed that Beckham was prepared to make the switch.
"That's exactly what happened, there really was this interest," Assumpcao told Lancenet.