The 34-year-old has been linked with a return to the Spanish side, who he joined Hamburg from on a free transfer in January 2010.
Van Nistelrooy’s current contract with Hamburg is set to expire at the end of the season.
The Hamburg boss told ZDF television: “I have been aware of that (the reported interest of Real) since Thursday now and I have already been in touch directly with Ruud about this link.
“We have not been receiving any bid from Real Madrid and I really do not want to miss Ruud, this is my point of view. I would want him to stay.
“Ruud is actually in a state of fitness he has never had before in his spell at our club.
“Him moving on would be a bitter loss for Hamburger SV. We are desperate to do everything we can to ensure he is going to remain here.
“Although I am absolutely able to understand his situation and viewpoints on all this, Ruud van Nistelrooy is a great player and person.”
