The 19-year-old has enjoyed another promising season, catching the eye in Schalke's run to the last 16 of the UEFA Champions League.
Reports in Germany earlier this season suggested Draxler was a target for both AC and Inter Milan, along with Chelsea and Manchester United.
Further speculation in the German media has seen Draxler lined up as the ideal replacement for Mario Gotze, who will leave Dortmund for Bayern Munich in a deal worth £32million this summer.
But the Germany international has denied the latest stories about his possible departure from the Gelsenkirchen club.
"I am a Schalke 04 player," Draxler declared. "I know some took this (Borussia Dortmund) rumour for granted.
"I felt sad about this, just because I am able to promise for all times that I will never play for Borussia Dortmund in my career. This is a fact!"
Schalke general manager Horst Held was equally adamant that the club want Draxler, whose contract expires in 2016, to stay with them for as long as possible.
He said: "Julian Draxler is a regular first-team player of our club, he is an important player for the future of Schalke 04.
"We do not intend to sell him at the end of the season. He likes being at Schalke 04, and he is fully behind the club. We want to keep him for as long as possible."