The 34-year-old striker was identified by Jose Mourinho as someone they could draft in on a short-term basis to cover for the injured Gonzalo Higuain.
Higuain is out for four months following surgery on his back, leaving Real short of attacking options.
Van Nistelrooy had been keen on a return to Madrid where he plundered an astonishing 46 goals in 68 games during an earlier three-and-a-half-year tenure.
But the Bundesliga club have blocked the move and want the veteran striker to help fire them up the table from their current sixth position.
"A contract extension with Hamburg can now be ruled out," his agent Rodger Linse told the Hamburger Morgenpost.
"He cannot understand it (why Hamburg did not let him go) and he has got a problem with it. It is very, very painful.
"It is sad because Hamburg have no idea what they are doing to Ruud with this decision."
Van Nistelrooy has scored six goals this season for Hamburg.
