United boss Sir Alex Ferguson snapped up the youngster in a shock £7.4million deal three weeks ago, despite having never even seen the 20-year-old play.
Bebe, who arrived at Old Trafford from Portuguese Premier League club Guimaraes, has not played competitive football at a level higher than his native third division.
And Jorge Paxaio, coach of the forward's former team Estrela da Amadora, claims the club offered him around Europe for just €150,000 as they urgently hunted cash to avoid a winding-up order last term.
"Last season we had no money at all," Paxaio told the Daily Mail. "We were trying to transfer Bebe to other clubs.
"We had to raise money desperately. We told everyone in England and in Europe: 'For 150,000 Euros you can have him'.
"We couldn't get anybody interested. Nobody trusted him. None of the clubs were interested because he had never played at a high level."
Bebe, who terminated his contract with Estrela and moved to Guimaraes on a free transfer in the summer, earned £12,000 a year with the third division club, the same sum he now takes at United in a week.
And Paxaio admits he would never have predicted the striker's move to Old Trafford.
"I was surprised with the sudden way it happened with United," he added. "I was hoping he would move to a bigger club in Portugal or a medium-sized club in Europe.
"I didn't expect Manchester United. Having said this, Manchester United have signed an extraordinary player."
United were only alerted to Bebe after he impressed during this year's pre-season with Guimaraes, scoring five goals in six games.
The player's former agent Goncalo Rels has reiterated that Ferguson could have picked up the forward at a much lower price if he had moved to sign him earlier.
"Bebe would have been very cheap during last season and then we tore up the contract because he wasn't being paid by Estrela and so then he was free," said Rels.
"A scout from United could have contacted me or the club last season. There was no secret.
"But I understand that the United scout just saw certain games in Portugal and only realised Bebe was a great player when he saw some pre-season games involving Guimaraes.
"If they had looked wider they would have seen him earlier and paid very little. But everyone was the same."