The 32-year-old failed to hold down a regular place at Anfield this season and has been linked with a move away from the club.
“If Liverpool get a new coach who wants to keep me and wants to give me more games than last season, then that is a possibility,” Kuyt told Bild.
“Yes. HSV is an option. I am proud that such a great, wonderful club have shown interest in me. But, there are other offers.”
Kuyt plans to decide on his future after next month’s Euro 2012.
Kuyt said: “Yes. Everything is settled with my agent Rob Jansen.
“My agent knows what I want. He controls everything for me.”
