The Sporting CP captain played for Amorim with the Portuguese giants.
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Sky Italia's Gianluca di Marzio is reporting Amorim has been pushing Old Trafford chiefs to move for Hjulmand.
The United manager believes Hjulmand's game is well suited to the Premier League and is convinced he will be a big hit in England.
However, any move will hinge on Amorim staying in charge at United. If he establishes himself long-term, Amorim will seek a reunion with Hjulmand.