Amorim has also verbally agreed personal terms with United, with the Premier League giants hopeful a deal can be concluded in time for him to take charge of the match against Chelsea on Sunday.
Barring any last-minute hitches, the United gig will be Amorim's fifth managerial role having previously worked at Casa Pia and Braga's first and second teams.
Amorim will take over a Red Devils side languishing in 14th on the Premier League table and in desperate need of a spark to kickstart their season.