Both Chelsea and Napoli have expressed interest in the 20-year-old Garnacho.
United did not respond to questions about the reported offer from Chelsea – said to be around £60m – that they are looking for.
The club has been open about the fact that the setting of its Profit and Sustainability Rules (PSR) is stringent and has written to a prominent supporters group to admit they are at risk of being breached unless costs are cut.
Under PSR rules, selling a local player like Garnacho creates more space in the submission process.
However, United know that such a move would go down poorly with fans who repeatedly chanted the Argentina international's name during the win over Rangers.
“Let's see in the coming days,” Amorim said. “He is a Manchester United player and he was very important for us today.
“I think he's improving in every aspect of the game, he was better today playing on and off the pitch as well, changing positions, working on improving his recovery position. Sometimes he shows some frustration and that's good because he wants more. He has the ability to do that.” Be much better in every situation in the game.”
Signed from Atletico Madrid in 2020, Garnacho has made 118 first-team appearances for United since making his debut in 2022, scoring 23 goals.
He has scored eight goals in 32 games this season, but with United's next home game not due until the day before the transfer window closes against Crystal Palace, was he bidding farewell to Old Trafford fans?
“The fans were making their feelings very clear. They love him. He keeps you on the edge of your seat,” former Champions League winner Rio Ferdinand told TNT Sports.
He added: “I don't think he was the one who initiated this step. I don't think he was the one who said: I want to leave.”
“But the system is going against him. Amorim doesn't play out wide, so you don't see the best of him. That will be one of the main reasons why they listen to offers.”
