The Austria Under 21 international has been linked with the likes of Arsenal, Liverpool, Juventus and Lazio in recent weeks.
The 21-year-old has now claimed that United are also tracking him.
“There is an interest from Manchester United and some big Italian clubs,” Hinteregger was quoted by the Austria Press Agency.
“I am honoured by it. Honestly, I did not think that it could happen so fast. My goal has always been to play with the Red Bulls, but of course such rumours are flattering.
“With my agent Frank Schreier, I need to consider if there are the conditions for a change and what prospects I would have with a move to a top team.
“I am not a dreamer and I know that these clubs have many interesting players who have no space to play.”
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?