The 20-year-old South Korean international is one of the most highly-rated young players in the Bundesliga, and has attracted attention from a host of top European clubs.
Spurs and Liverpool are thought to be tracking the forward, while Borussia Dortmund and Bayern Munich reportedly remain keen to keep him in Germany.
Still, the South Korean international insists he's happy at Hamburg, and has no plans to leave at the moment.
"I think in two or three weeks I will know more," Son told regional newspaper Hamburger Morgenpost. "Why should I not stay here?"
The 12-goal attacker has a year remaining on his Hamburg contract, and the Bundesliga club would not want to lose him on a free transfer following the 2013/14 season.
Ex-Tottenham playmaker Rafael van der Vaart has advised his Hamburg teammate to stay put and ignore interest from the Premier League.
But Hamburg finished seventh in the top flight this season, just outside the European qualification spots.
With Europa League football on offer at Tottenham, Son may be tempted to swap the Bundesliga for the Premier League this summer.