The 20-year-old, who has scored five league goals this season, is regarded as one of the best players to emerge from Asia in recent years.
Liverpool have been strongly linked with the striker in recent weeks and he has seemingly opened up a move to the Premier League.
"I am yet unaware if I am to sign a new deal with Hamburger SV this winter," he told the Hamburger Morgenpost.
"Still there is no doubt I am very happy about the circumstance of being a player of Hamburger SV. I like the club and I love the fans as much as they love me."
Son's current deal will expire in 2014.