The Austrian spent 12 months at Oakwell, helping the club miraculously escape relegation in 2019-20 before departing for New York Red Bulls with only a handful of games played last season.
Reports last week claimed that new United interim boss Ralf Rangnick wanted to bring Struber to Old Trafford as his assistant but that approach has been rebuffed by Struber and New York Red Bulls.
The 44-year-old has previously worked with Rangnick at Red Bull Salzburg but says he is happy in his role with Red Bulls in the MLS.
"There has been a request," Struber told Sky Sports in Austria.
"It's no secret that Ralf Rangnick and us know and appreciate each other.
"At the same time I have a job 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."
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