On the back of Michael Carrick's departure and with several familiar faces already in jobs, Rangick acknowledged last week that he would need to look elsewhere for support.
Reports emerged that Struber, a former manager of Barnsley, had been contacted over taking a key role on the 63-year-old's coaching team.
However, Struber is remaining Stateside, telling Austrian Sky Sports: "There has been a request. It's no secret that Ralf Rangnick and us know and appreciate us well and appreciate very much.
"At the same time I have in New York, which also makes me look very hopefully into the future and therefore I do not want to give up with New York overnight. I have a longer-term contract there and still have a lot of goals with an ambitious team."
The Red Bulls finished in seventh place in the Eastern Conference this season, eventually losing in the first round of the MLS playoffs. body check tags ::