Director of football Frank Arnesen has confirmed the club have spoken to the Dutchman's agent about the possibility of a summer move
Kuyt has become a fan favourite at Anfield since arriving from Feyenoord in 2006, but has struggled to hold down a regular first team place this season.
Reports in recent weeks have suggested Liverpool might be looking to offload the Dutchman in the summer, and Arnesen believes Hamburg have a good chance of signing him.
"We were not told that Dirk Kuyt doesn't want to come here," he told reporters.
"He is an experienced player that could help our young players a lot.
"If he decides to leave Liverpool, there are some good arguments for Hamburg."