Uncertainty surrounds future of Son
Hamburg's South Korean forward Son Heung-Min hit his sixth goal of the season to lift his side into the top half of the table and spark further speculation about his future.
Son, 20, grabbed the only goal of the game to see off Mainz 1-0, putting away a cross from Maximilian Beister who appeared to be in an offside position when he delivered the ball.
The €10 million-rated forward is under contract with Hamburg until 2014, but is reported to be attracting interest from clubs including Arsenal and Liverpool.
Reports have suggested he could be on the move in January, but Die Welt quoted him as saying: "My agent won't tell me anything about it.
"It's difficult for me. I am under contract until 2014 and have to discuss things with my dad and my agent."
Hamburg general manager Frank Arnesen has said the club faces a huge battle to keep him.
Arnesen saw Hamburg benefit from a few refereeing decisions against Mainz, who were refused what looked a penalty when Michael Mancienne brought down Adam Szalai in the box.