The Dutchman is currently in charge of the Red Devils on an interim basis, having been given the job last week due to Erik ten Hag's dismissal.
Van Nistelrooy has now had two games at the helm, guiding the team to a 5-2 victory over Leicester City in the EFL Cup on Wednesday night, before overseeing a 1-1 draw with Chelsea in the Premier League on Sunday afternoon.
The club's former striker will again lead the team against PAOK and Leicester, before Amorim arrives from Sporting Lisbon as Ten Hag's permanent replacement.
Amorim has confirmed that he will be bringing staff members with him to Old Trafford, meaning that there is huge uncertainty surrounding Van Nistelrooy's future with the 20-time English champions.
Van Nistelrooy suggests he will be staying at Man United
Speaking after the 1-1 draw with Chelsea, Van Nistelrooy hinted that he will be remaining at Old Trafford under Amorim, although the Dutchman stressed that he had not yet spoken with the incoming head coach.
"I look forward to get to know him better, he has done very well in Portugal, young talented coach, done well over a longer spell in Portugal. Looking forward to keep helping the club forward, that's my main goal," he told reporters during his press conference.
"Over the coming days we will be in communication and I am waiting for that. What is more important is that we are in training tomorrow and prepare for the game on Thursday. I haven't spoken to him [Amorim] yet but it will happen. You saw today that we competed well against a very good side. This is the way forward for this group of players."
In a separate interview with Sky Sports News, Van Nistelrooy said: "We are behind the new manager, everyone at the new club is focusing on the two games that are coming which are very important but then we will work hard to make this club better every day."
Van Nistelrooy: "It's special to be back in the city"
Van Nistelrooy celebrated Bruno Fernandes' penalty against Chelsea on Sunday with pure emotion, and the Dutchman also opened up on the "special" feeling that he has had since returning to Man United as assistant manager over the summer.
"I came here to help the club in any capacity. After these two games that will continue and hopefully it can work out," he told BBC Sport. "It's special to be back in the city and at the club. I really enjoy every single minute of it.
"I try to share the culture of the club, the culture of the town and the fans. That's an important part. I'm glad I can share these moments and help the players understand the spirit. I saw the spirit on the pitch on Wednesday and today. That's the foundation to grow."
Man United could not hold onto their lead against Chelsea on Sunday, though, with Moises Caicedo's volley earning the Blues a share of the spoils in what was a largely low-key affair in Manchester.