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United need more firepower as they look to win the Premier League title for the first time since 2013, back when Sir Alex Ferguson ruled the roost.
Cristiano Ronaldo and Wout Weghorst are no longer at the club, while Anthony Martial has long been too inconsistent.
Though Marcus Rashford can play down the middle, the England international would prefer to be deployed on the left wing instead.
United are keeping tabs on Atalanta hitman Hojlund, who scored nine goals for the Serie A side last season.
But while the club are mulling over sending Greenwood to Italy on loan as part of a swap deal, no final decision has been made just yet.
