The Bundesliga giants and Champions League finalists also want to retain Jadon Sancho permanently.
United are eager to sell both Greenwood and Sancho, but the issue is agreeing a fee with Dortmund.
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According to ESPN, Dortmund would prefer a loan deal, which is also the case with Sancho.
However, United want to sell the troubled young star, who they will not reintegrate into their first team.
Greenwood had an impressive season on loan at Getafe in the Spanish La Liga this season.