The Red Devils are desperate to land a new number No.9 this summer and set their sights on the promising 20-year-old who is valued at a staggering £86million.
Financial constraints are in place for the club following the recent £60m acquisition of Mason Mount meaning the club had no choice but to offer players as part of the package.
The Athletic report that Atalanta rejected United's offer, making clear they will consider a cash-only deal.
The Denmark international netted 10 goals in 34 appearances during his breakout season for the Serie A side.
It is unclear which players were offered in the package but it is understood that United would not stand in the way of an exit for both Fred and Donny van de Beek.
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With a move for Harry Kane seemingly out of the question, Hojlund is now United's top priority while France star Randal Kolo Muani still remains an option.
In addition to recruiting a new striker, United have pinpointed a new goalkeeper after the departure of long-standing No.1 David de Gea.
The Red Devils are expected to intensify their efforts to land Inter goalkeeper Andre Onana who is believed to be keen on the move.
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But the clubs are still some way apart in their valuation of the shot-stopper with Inter holding out for a £51m fee.