Manchester City, Manchester United and Chelsea all also scouted the striker, with the player's representative hinting at a possible future move to the Premier League
The 20-year-old scored 12 goals in 33 appearances for Hamburg last season before joining Bundesliga rivals Leverkusen in a deal with €10 million [£8.5m] - with the player revealing he turned down Champions League runners-up Borussia Dortmund to seal the move.
|1/1||Leandro Damiao is 1/1 with BetVictor to sign for Tottenham
"Liverpool, Tottenham, Fulham, Southampton and Cardiff were interested in concrete terms," Son's agent, Bliemeister, told Bild.
"Manchester City ... Chelsea and Manchester United have observed Son. I think, at clubs like Liverpool and Tottenham, he would also be able to play. I think Leverkusen, for the next two or three years, is the right step to develop.
"Son feels at home in Germany and in the Bundesliga. He speaks the language perfectly. Surely the Premier League could someday be the goal, but the Premier League is getting better and more interesting."
Tottenham are chasing a striker to freshen up their strikeforce - with Leandro Damiao and David Villa targeted - while Liverpool could lose Luis Suarez after the Uruguayan spoke of his desire to join Real Madrid.