Kuyt, 31, has a year to go on his current deal at Anfield but there is speculation he could leave the club in the summer after six years in England.
Fink is a big admirer of the former Feyenoord man, and he told www.kicker.de: "He has class, and he is also a fighter. There is nothing more that needs to be said about the quality of this player. Whether this is something we feel we want to commit to, we will see."
The comments from Fink, who has steered Hamburg to Bundesliga safety after the club endured a dreadful start to the season, follow similar sentiments from the club's technical director Frank Arnesen a couple of weeks ago.
"A player like Kuyt, who is still in good shape, can add something to any team," the Dane told Bild.
"He is a real team player with an excellent attitude."