The Netherlands international was linked with clubs such as Liverpool and Arsenal in the past few months, but he eventually decided to sign a two-year extension to his expiring contract with the Konigsblauen instead.
"A number of clubs from England enquired about me. However, I never opened contract talks with any of those teams," Huntelaar told Welt.
"I asked myself whether I wanted to stay put or make the move to England. The Premier League is the only top league in Europe where I have not played yet.
"The most important thing for me was that my family feels well, though. And we have everything we need here at Schalke."
The 29-year-old then went on to discuss his long-term future, and made it clear that he wants to end his professional career at Ajax.
"My dream club has always been Ajax. I might return there towards the end of my career before I retire. I am completely focused on Schalke for now, though."
Huntelaar previously wore the Ajax jersey from January 2006 until January 2009.