The 19-year-old told Bild: "I had sleepless nights about it. I was on holiday in Egypt with my girlfriend and sat alone on the balcony thinking about what to do.
"It was not an easy decision. You never know whether you will ever get such an offer again. In the end, I followed my heart and decided to remain at Schalke."
The German international also declared that he would never be persuaded to sign for Schalke's bitter rivals Borussia Dortmund.
"Unless they brainwash me, I will never join Dortmund," he said.
Schalke have included a £39.3m release clause in Draxler's new contract, which runs until 2018.