The 32-year-old is approaching his 10th year in North London and has made more than 500 appearances for the club without winning a trophy.
Son was asked about his legacy and how he wants to be remembered when he eventually leaves the club.
"Being at one team in 10 years is a good effort, I think. You have to be consistent with this and you also have to give something back to the club.
"I still don't think I am a legend of this club. I have said I want to win something with Spurs, then I want to be very happy to be called legend.
"I joined Spurs to win a trophy and I hope we can make a special season."
Spurs have not won a major trophy since the League Cup in 2008 but while a trophy is the goal, Son has not set a personal target for this season.
"I am not setting a goal of where I should be.
"Imagine if I say 10 goals or something and you score 10 goals in six games, your goal is done. I want to push as much as I can, never feeling it is enough.
"I want to go as high as possible in every aspect – team, individual, everything. Then we will see where we are at."
The winger has scored at least 14 goals in each of the past eight seasons and will be hoping that his efforts do not go to waste as the club chases their first trophy in over 15 years.
