The Cottagers are weighing up a move for the Denmark international as Rodrigo Muniz is the subject of bids from Atalanta.
AC Milan have been in talks with United for Hojlund and have offered a £4.5million loan fee with an option to buy for £39m.
However, Hojlund has been digging in his heels saying he wants to stay and fight for his place - despite Benjamin Sesko arriving for £73million as part of a new look £200m frontline.
Fulham would need to know Hojlund wants to come before making a suitable offer.
So far, Hojlund is backing himself to still make a contribution to Ruben Amorim's squad and to be ready regardless of whether Sesko fails to hit the ground running.