Rangnick was appointed as United caretaker when Ole Gunnar Solskjaer lost his job a few years ago.
While he came in with a big reputation, he struggled to win over the players or fans.
Asked why he turned down an assistant role in that setup, per The Sun, Struber stated: “I was only one year at this time in New York and he called me to ask me to come with him to Manchester United to be first-team coach.
“But it was not the right moment for me. I was a head coach and I think he was initially only on a contract for half a year, so nothing was clear for after that.
“Also, they gave him maybe not the biggest power and it was more of a caretaker role and I thought, especially at Manchester, that these boys needed a manager. That was very clear.
“So it was not the right moment but I had a contract in New York.
“I’d left Wolfsberger after half a season, then I moved from Barnsley after one season and it would have been moving from New York after one season - this would paint a picture of me that I didn’t want.
“And, I also see myself as a head coach, not an assistant coach.”