The 27-year-old was dropped by United boss Amorim for Sunday's win at Manchester City and responded by saying he was "ready for a new challenge" in an interview on social media.
Rashford came through United's youth ranks and has chalked up 138 goals in 426 appearances for the club since making his debut in 2016.
However, he has lost form over the last 18 months with United and was also axed from England's Euro 2024 squad.
Rashford has scored just 15 goals in 67 appearances since signing a lucrative new contract 18 months ago, with speculation over his future increasing in recent days.
The forward, who was absent from training on Monday through illness, is set to miss the League Cup quarter-final at Tottenham on Thursday.
Amorim is keen to keep Rashford but he admitted he would have handled the situation differently when he was a player.
"If this was me, probably I will speak with the manager," he told reporters on Wednesday.
"But, guys, let's focus on Tottenham. Tottenham is the most important thing."
Amorim revealed he has yet to speak to Rashford since the interview that threw his United future into doubt.
'A little bit emotional'
"It's hard to explain to you guys what I am going to do," Amorim said. "I am a little bit emotional, so in the moment I will understand what to do.
"I am preparing the game and then we will see. Let's focus on the team not individual players. That's it."
Amorim's 14-minute press conference featured 16 different questions about Rashford.
It was an indication of the intense media scrutiny Amorim will have to get used to at United after arriving from Sporting Lisbon to replace the sacked Erik ten Hag in November.
"It's a hard situation to comment on," he said. "If I give a lot of importance, it will have big headlines in the newspaper.
"If I say it's not a problem, then my standards are getting low. So, I will deal with that, I understand that.
"My focus is not to take the attention from the game, from the team, what we did in the last game and put on Marcus.
"What I'm saying is that the team is more important than the individual. We will assess at the right time, let's focus on the game. That's all."
Amorim is determined to concentrate on the Tottenham clash despite the focus on his controversial decision to axe Rashford and Argentina winger Alejandro Garnacho from the Manchester derby.
Unlike Rashford, Garnacho was pictured with the United squad heading to London for the quarter-final having reacted impressively to his exile.
"Really good, he trained really well," Amorim said of Garnacho. "He seems a little bit upset with me and that is perfect.
"I was really, really happy because I will do the same in his position and he's ready for this game."
© 2024 AFP