The Dutch international has fallen out of favour at Anfield this season and could leave over the summer, amidst reported interest from his former club Feyenoord.
The Dutch outfit previously admitted they would find it tough to land Kuyt this year but hoped to do a deal when he decides to call it a day with the Reds.
However they have been encouraged in their pursuit of the 31-year-old, who has fallen down the pecking order at Liverpool and may walk away from the club sooner than planned.
Kuyt was left out of the Liverpool’s starting line up for their FA Cup semi-final showdown against Everton last weekend, with the forward expressing his displeasure on missing out on the occasion.
However according to De Telegraaf, Hamburg are said to be ready to enter the race for his signature and could launch a bid this summer.
The paper also reports interest in Kuyt’s signature from Italy, with both Fiorentina and Roma monitoring the situation as the season draws to a close.
Hamburg could offer him a route to the Bundesliga however, with the German club said to ready to offer him a lucrative deal that would equal his current deal with Liverpool – something other clubs interested in his signature would be unable to offer.