The 21-year-old forward was allowed to leave Old Trafford at the end of the summer transfer window. After a long-running internal investigation, it was decided that Greenwood had no immediate future in Manchester.
He was linked with clubs in Italy, Turkey and Saudi Arabia, but ended up agreeing a season-long switch to Getafe.
England international Bellingham was already in La Liga by that point, having completed his own €103 million (£88m/$110m) move to Santiago Bernabeu, and he apparently suggested that Greenwood follow a similar path.
Bordalas has told Radio Marca: “Greenwood is friends with Bellingham, and he advised him to come to the Spanish league.”
Greenwood has not played for United since January 2022, following his arrest on suspicion of attempted rape, assault and coercive control.
Bordalas added on acquiring the player, who has 22 Premier League goals to his name: “It was a surprise, we never thought we could get a player like that.
“But they got in touch with our sporting director (Ruben Reyes), we talked, we didn’t think it could happen but both sides made an effort [financially].”
Greenwood has been well received by Getafe supporters and could be handed an immediate debut for the club in their meeting with Osasuna on Sunday.
He is some way short of match fitness and sharpness, but Bordalas added on a player that he has billed as the “Golden Boy”: “He is a fantastic player. You have to be patient, calm, he hasn’t played in a year and a half.
“We and his colleagues are helping him. He is integrating in a sensational way and I hope he can help us.”