With Real's Argentina striker Gonzalo Higuain out for the next four months with a back injury, 34-year-old Dutchman van Nistelrooy, who is out of contract at the end of the season, has been targeted as a replacement.
"We will not let him leave," said Reinhardt. "He will see out the end of his contract, the decision is final."
Van Nistelrooy scored the winning goal in Hamburg's 1-0 win over Schalke 04 on Saturday which left his side seventh in the league and admitted he was torn between Hamburg and Madrid.
"It has been a strange week. It is not just any club which have expressed interest, it is Real," he said. "They are the only club which can make me change my mind."
With strikers Mladen Petric and Paolo Guerrero both carrying injuries, and Heung-Min Son at the Asian Cup with South Korea, Hamburg need to keep hold of their Dutch star who joined them from Real in January 2010.
Hamburg need a top five finish to be sure of a place in Europe next season.