Son is reportedly one of Tottenham's main targets this summer, and the club were thought to be confident of signing the South Korean international for £10m.
But Borussia Dortmund have emerged as a potential rival following confirmation of the sale of Mario Gotze to Bayern Munich at the end of the season.
The 20-year-old Germany international will swap one Champions League finalist for another this summer, and Dortmund believe Son could be the man to replace Gotze.
Son, also 20, is regarded as one of the best young players in the Bundesliga, and is Hamburg's joint-top league goalscorer with 11 goals.
The South Korean is out of contract at the end of next season, and despite Hamburg's offer of a new deal around £45,000-a-week, he's yet to put pen to paper.
The report claims Son's first choice is a move to White Hart Lane, but Dortmund's interest complicates matters, offering him the opportunity to stay in Germany where he's settled well.
Add to that the fact that Dortmund are all but guaranteed to qualify for next season's Champions League, while Spurs are struggling to secure a top finish, and Son's decision could swing back in favour of the German giants.