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."