Rangnick is expected to be confirmed as the temporary successor to Ole Gunnar Solskjaer imminently, though will not take charge of Sunday's Premier League trip to Chelsea while awaiting a work permit.
The 63-year-old is ready to sign a six-month contract, after which he will take on a consultancy role at Old Trafford and influence the search for Solskjaer's long-term permanent successor.
The former Schalke 04 and RB Leipzig manager is considered the 'godfather of gegenpressing', influencing the coaching careers of Jurgen Klopp, Thomas Tuchel, Julian Nagelsmann and many more of European football's leading managers.
An inability to press effectively was one of the major criticisms of Solskjaer during his final months in charge, particularly following the return of Cristiano Ronaldo, who is one of the least active pressers in Europe's top five leagues.
Carrick, however, believes that the United squad will be able to adapt to and implement Rangnick's philosophy.
"Listen, there's a lot of different styles in football," the United caretaker said.
"There's a group of players here, whoever comes in they can adapt. There are some really good people and human beings in the squad and I'm sure they'll look forward to what's ahead."
Carrick refused to be drawn at length on Rangnick's imminent appointment, insisting that he has only been focused on Sunday's game against Chelsea and had not given much thought to whether he and the rest of the coaching staff will stay on.
"I think as you can appreciate this week's been quite busy already and, again, as I said before, I haven't really had time to think, I haven't given it much thought.
"I'm preparing team to best I can and I've given everything I can, anything after Sunday is not in my thoughts at the moment."
"Speculation and reports are speculation and reports. As I'm sitting here now I'm preparing the team for the game, I haven't got any more news to share with you on that front."
"For me, to be sitting here talking about too far ahead, my thoughts are on the game on Sunday, it has to be.
"Coming in this week and having a laser focus on two games, the challenges it focuses, I can't get distracted by anything else, anything else will take care of itself in the coming days and weeks ahead."
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies