The Dutchman, who will be 32 in the summer, has had fewer first-team opportunities this season and is being linked with a move at the end of the campaign.
Kuyt has a year left on his remaining contract at Anfield and while former club Feyenoord are believed to be keen to take him back Arnesen has spoken publicly about the striker.
"A player like Kuyt, who is still in good shape, can add something to any team," he told Bild.
"He is a real team-player with an excellent attitude."
There had been suggestions initial negotiations had taken place but Kuyt's agent said that was not the case.
"There have not been any talks with Arnesen or with someone else from HSV," he said.
"Would Kuyt be interested in a move to the Bundesliga? I can't say anything about that.
"A lot of clubs have made enquiries, but there's nothing concrete for now."