The 29-year-old former Hamburg midfielder has been linked with a return to Germany, where his wife still works.
Asked about the prospect of joining Schalke, Dutchman Van der Vaart told Bild: "I don't know. Actually, I want to stay at Tottenham. But, in football, you never know."
Pointing out he never expected to join Spurs or Real Madrid in the way he did, he added: "I spent three years living in Hamburg and had a wonderful time at HSV.
"My wife, Sylvie, works there and we have many friends who live in your country."