The 26-year-old defender is a wanted man after forming part of the Germany squad that tasted World Cup glory in Brazil this summer.
Clubs across Europe are reported to have expressed an interest in his services, with Premier League clubs leading the chase.
Howedes concedes that a new challenge outside of his homeland may appeal at some stage in the future.
He is, however, happy where he is for now and has no intention of breaking a contract that is due to run until 2017.
Howedes told Deutsche Presseagentur: “There are always rumours in football, especially when you have won the World Cup as a player. I am definitely not after such rumours at the moment.
“I am facing my responsibilities as a player of Schalke. I have played for Schalke since I was 13 years old and would not have been here so long if I did not love the club.
“Of course, I have said that it would be flattering to move abroad one day in the future – to learn a new language, to get used to a different club and new surroundings - but there is plenty of time for that.”