HSV have sacked Steffen Baumgart after their 2-2 draw with Schalke 04.
And the 2.Bundesliga club are being linked with a move for Van Nistelrooy as a replacement.
Van Nisterlooy is also interesting Leicester City and Coventry City, which are also seeking new managers.
Meanwhile, Baumgart has said today: "I would like to thank Stefan Kuntz and also Jonas Boldt for the opportunity to work in the team that I have loved since I was a child.
"It was an exciting and very intense time, I will remain attached to the club and hope it achieves its goals. My thanks also to the staff and employees of the administrative part."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play