The English football club was looking to strengthen their midfield this summer, but the transfer window has now closed, and their efforts have been fruitless.
According to reports, Amorim's side made a late offer to sign Gallagher, 25, from Atletico Madrid, but the Spanish club was unwilling to consider a loan deal, insisting on a permanent sale.
Manchester United had previously considered other options, including Carlos Baleba from Brighton, but were deterred by the South Coast club's high price tag of £100 million or more.