South Korea international Son is said to be interesting a number of clubs in the Premier League, with Tottenham, Chelsea, Liverpool and Arsenal all said to be keen.
Reports suggest that Spurs sent scouts to watch the 20-year-old in action on Wednesday as he appeared for his country in a friendly date with Croatia at Fulham's Craven Cottage.
It has been suggested that Hamburg would be looking for around £10million for their highly-rated frontman.
General manager Frank Arnesen has refused to speculate on a price, but admits a tempting bid could force the club's hand.
He is, however, hopeful that fresh terms can be agreed with Son, allowing him to remain in Germany for the foreseeable future.
Arnesen told Hamburger Morgenpost: "Of course we have an acceptance limit.
"But Sonny is a very young and great talent. We have the ambition to sign new terms with him and will be in a position to hand him a good deal.
"I am sure we can find a solution to keep hold of him for longer than the end of his current deal (which expires in June 2014)."
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