Schalke 04 hitman Kuranyi has drawn the attention of Martin Jol this term after notching 13 goals, although he couldn't establish himself as a regular.
"I have heard about these rumours." the 27-year-old, who was previously tipped to join a Premier League club in January, told Sport-Bild.
"It is true, they (Hamburg) have enquired."
New Structure
In the meantime, Schalke skipper Marcelo Bordon revealed that he had changed his mind about leaving the club.
The veteran centre-back was planning to depart in the summer, but he backtracked on his decision when Felix Magath was announced as the Konigsblauen's next boss.
"I have two years to go on my contract and I have the intention to help the team," Bordon told West German Broadcasting.
"When there comes such a manager and presents a new structure and way of organization to a club, as a player you would like to share that experience.
"Although I am injured at the moment I am feeling well enough to continue for the club. But Magath is the new manager and he has to make these decisions of those who are leaving and who are not leaving the club."