The attacking midfielder had a hard time deciding whether he was ready to move abroad, while he has ruled out joining Borussia Dortmund at some point.
The Germany international reportedly received offers worth up to 60 million euros over a five-year period earlier this summer, but Draxler eventually opted to stay at his current club as he felt the time was not right to move abroad yet.
"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," Draxler told Bild when questioned about Madrid and City's offers.
"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 19-year-old then went on to discuss a potential transfer to Borussia Dortmund and again stressed that he would never leave Schalke for the club's arch rival.
"Unless they brainwash me, I will never join Dortmund."
Draxler has a contract with Schalke until June 2018, but has a 45.5 million euros release clause.