Sky Sports News has learned that there is strong backing to retain the 48-year-old at Carrington in a different role once his stint as interim manager comes to an end.
Van Nistelrooy is esteemed by United's leadership group for the way he carries himself, along with all the staff that serve first-team operations.
No concrete decisions have been taken on the make up of Amorim's backroom team yet, but the incoming head coach does want to bring in five of his colleagues from Sporting, including his long-time assistants Carlos Fernandes and Adelio Candido, as well as the experienced Emanuel Ferro who operates in that role.
If they are to join, it is hard to see how Van Nistelrooy, who has an assistant manager contract, can still fill that position.
TrendingSome tweaking of his responsibilities would be required to keep him at United, but the club legend has stressed his openness to helping in a different way. He has also thrown his support behind Amorim, and has said on more than one occasion that he would love to speak to him.
Beyond Van Nistelrooy, there is also a strong desire for Darren Fletcher, currently first-team coach, to remain under Amorim.
He has been a great link between the academy and senior side, having taken that same journey as a United player - making over 300 appearances and winning 13 trophies in 20 years.
One source said: "The work Fletcher does may not be the spotlight, but it has been important."
pundit Jamie Carragher has warned Amorim that he should not listen to the players when deciding if Van Nistelrooy should be kept on.
"I don't think the players should have any say in anything like that. Certainly with the performances they've given in the last few years. If it was a highly successful team and you had huge respect for the players within the dressing room and you valued their opinion, that might be something you take into consideration.
"You don't let players start calling the shots, and certainly not players at Manchester United."
Asked for his own thoughts on Van Nistelrooy staying, Carragher added: "I don't think there's a yes or no to that.
"I'm sure he's got his team that he'll bring over from Sporting. If he feels he needs a connection, someone who knows Manchester United, someone who knows the squad who's been there for the last few weeks.
"He may actually say, 'Can you actually stay with me till the end of the season? Give me a background of how this club works, what it was like in the past, what it would have been like this season under Erik ten Hag, what are the players like, how did he train?'
"So I think it would be a clever move to keep him for now. I don't think he necessarily has to keep Ruud van Nistelrooy for the long term, but I think the clever play would possibly be to keep him till the end of the season."
Roy Keane has warned incoming head coach Ruben Amorim that Manchester United are "average at everything" following their drab 1-1 draw with Chelsea.
United's new-manager bounce fell flat in a stale 1-1 draw with Chelsea at Old Trafford that confirmed their worst start to a Premier League season.
Ruud van Nistelrooy, United's interim boss until Amorim arrives on November 11, was unable to help spark the team into form as they played out a dismal draw with the west Londoners.
"He should have signed a longer contract," said Keane when asked about Amorim's appointment. "There is a long way back for this team.
"This is an average Manchester United team. All the stats back that up. They are hit and miss - you never know which team will turn up. Not good.
"'Boring' seems a bit strong but they lack conviction. It's really disappointing. It's so flat. This team is way off it, getting back in the top four.
"You look at certain individuals and they think they're better than they are. United are average at everything. There is nothing special about them.
"It was very quiet at Old Trafford. I was glad when the referee blew the final whistle."