Amorim is unconvinced by his current options as he seeks an attacking left-sided wing-back for his 3-4-3 system.
Sky Deutshland's Florian Plettenberg is reporting that United are pushing to sign Bayern Munich's Bosman prospect Alphonso Davies.
However, the Canadian isn't the only candidate, with AC Milan wing-back Theo Hernandez also under consideration.
Plettenberg states: "The search for a new left-back at Manchester United is in full swing. Highest priority for Ruben Amorim as reported!
"Alphonso Davies remains the desired target but difficult to realize
"Theo Hernández is also on the list alongside other options. However, Hernández is being closely monitored. Contract with AC Milan until 2026."