Jose Bordalas claimed earlier this week that Greenwood signed for Getafe on loan after Real Madrid star Bellingham 'advised' him to make the move, adding that the two are friends.
He told RadioMarca about signing the striker on loan from Manchester United: "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 is friends with Bellingham, and he advised him to come to the Spanish league."
Greenwood made his Getafe debut on Sunday, coming off the bench to make a late appearance off the bench in a 3-2 victory over Osasuna.
He had a hand in the victory, forcing the corner that led to Nemanja Maksimovic's winning goal in the 86th minute.
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But, after the match, Bordalas backtracked on his previous comments about an apparent link between Greenwood and Bellingham, admitting he got it wrong.
The Getafe head coach explained: "I had said that Mason Greenwood came to Getafe because he had spoken with Jude Bellingham.
"They have clarified to me that it was not the case."
Greenwood's late cameo against Osasuna was the striker's first competitive appearance for 20 months having been suspended by Man United in January 2022.
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The Premier League giants shipped Greenwood out to the Spanish club on loan after confirming in a statement it had been agreed he would 'recommence his career… away from Old Trafford' after an internal investigation into his conduct.
The 21-year-old was charged with attempted rape, assault and controlling and coercive behaviour, but those charges were dropped by the Crown Prosecution Service in February.
The club announced in August that he would leave and eventually joined Getafe on loan on deadline day.
Greenwood is under contract at Old Trafford until 2025 but he is not expected to play for Man United again, with the club set to consider permanent offers for the striker in the future.