Chief executive David Gill has revealed that United's pursuit of Bebe only gathered pace during the course of this week.
The Reds stunned football by announcing the prospective capture of the largely unknown Portuguese winger on Wednesday evening, and Gill sees the deal as further proof of United's investment in raw potential.
"He's a player we've been following, but he really came on the scene in the last week or so," Gill told MUTV. "We looked at him, spoke to a number of people about him and then went out and secured the deal yesterday.
"It's exciting. He's a potential player, and a lot of Manchester United's focus is about getting players who have the potential and then getting them under the great coaching of Alex, Mick, Rene and other people. He can fulfill that potential with Manchester United and I think it's going to be exciting. Let's hope it works out."
Bebe's arrival hinges on a successful medical later this week, and Gill moved quickly to play down suggestions the 20-year-old will be immediately sent out on loan. Instead, Bebe will be given the chance to assimilate and prove himself at United.
"He'll join up and be part of the first team squad this season," said Gill. "I think he'll probably stay this year. (He is) a boy who has to learn English and integrate into Manchester United, and he's really come from nowhere in a lot of respects.
"I think he'll benefit from having day to day coaching from some of the best coaches in the world in the Manchester United way. He'll certainly be with us this season and you never know, we'll see what happens."
David Gill was speaking at the launch of Manchester United's new partnership with Thomas Cook Sport.