Armas, whose last job was head coach of Toronto FC, would need a work permit before sealing a move to Old Trafford.
Sources have told ESPN that Rangnick is being allowed to appoint a “small number” of his own coaching staff to work alongside Mike Phelan and Kieran McKenna, both of whom were part of Ole Gunnar Solskjaer’s backroom team.
Another of Solskjaer’s assistants, Michael Carrick, left the club after taking charge of the team for three games before Rangnick’s appointment as interim coach until the end of the season.
Rangnick was asked about the possibility of bringing in his own staff at his official unveiling ahead of the win over Crystal Palace and said any appointments may take time to arrange.
“I’m more than happy to work with the current coaching staff because I need their experience, I need their expertise regarding the current squad,” he said.
“I will obviously try to find one, two, maybe three people who can join us in one or two weeks but due to the Brexit regulations it’s not too easy.
“Many of my former colleagues, no matter if it’s video analysts or assistant coaches, are in long-term contracts with big clubs so they are not available right now and we have to be a bit smart and clever and find the right people.
“I hope that we can get them in here in the next one or two weeks.”
Former midfielder Armas was capped 66 times by the USMNT before ending his playing career in 2007.
In 2008, he took an assistant coaching job at Chicago Fire and has also worked at New York Red Bulls as both an assistant and head coach.
Rangnick was appointed head of Red Bull’s global football projects in 2019.