The South Korea international's current deal is running down and due to expire in June.
However, Spurs hold a 12-month option in the contract, which they will trigger if an agreement cannot be struck before January 1.
Yesterday at his Europa League presser, Son was asked about the situation and said: "We haven't spoken about anything yet, but for me it was already all clear.
"At my age every second is a goal, we are in many competitions and I am focused on all situations. We want to win something, this club and all the people who gravitate around it deserve it. And for this work.
"Then in the future you never know what can happen, but I want to assure you that I will give everything for a club where I have been for 10 years and I have always done so. We'll see."