The 20-year-old has been a target for Arsenal over the past 12 months and they showed an interest both last summer and in January.
But with four years left on his current deal he is showing no signs of wanting to leave Schalke - with any club wanting him already knowing his release clause which stands at €45.5million.
Speaking to Bild, he said: "Of course, I am expecting some unverified rumours coming up throughout this summer. But it is very, very likely I will play for Schalke next season.
"I am able to seriously confirm I do not have any thoughts on leaving the club this summer!"
Draxler, who is going to the World Cup with Germany, helped Schalke secure third spot in the Bundesliga at the weekend with a 4-1 win over Nurnberg earning them a place in the group stage of the Champions League next season.
A product of the club's youth system, he became the youngest Schalke player to make 100 Bundesliga appearances recently while he has already been capped 10 times by his country.