The 22-year-old's contract with the German outfit expires in the summer, with the player being linked with a move to the Premier League.
Schalke face Arsenal on Wednesday night in the Champions League and Holtby, who has an English father, admits that he would jump at the chance to play for the Gunners.
"For me it was always a dream to play in the Premier League and it was always a team like Arsenal that I would like to play for," said Holtby. "Now I play for Schalke and I am happy to be here.
"My agent is there to handle the rumours. I want to put all my concentration on football. I'm a Schalke player and I cannot be fussed in my head with other clubs who want to sign me or whatever.
"That's not my interest. I want to have a good season with Schalke and give my best each week and if my head is with other clubs or the Premier League or England then I would not be myself."
Schalke 04 travel to Arsenal for their Group B clash on Wednesday.