The 31-year-old has struggled to hold down a first team place at Anfield this season, with recent reports suggesting that he will depart the Premier League in the summer.
"We were not told that Dirk Kuyt doesn't want to come here. 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," Arnesen told reporters.
Kuyt has made 276 appearances for Liverpool.