Reports in England have suggested that the Gunners are set to make a £21m offer for the 22-year-old, who has one year remaining on his contract at the Bundesliga club.
Goretzka has started both of Germany's matches at the Confederations Cup in Russia so far, scoring in the 3-2 victory over Australia.
Speaking in Sochi, Goretzka is quoted by Sky Sports News as saying: "I do not want to say anything about the transfer rumours, I'm focusing on the Confederations Cup.
"I'm not going to give state-of-play updates, but if there are facts, I will announce them.
"I'm not the type to be impressed by newspaper reports, I know what my qualities are, but I will not build myself up."
Goretzka, who has won seven caps for Germany, joined Schalke from hometown club VfL Bochum in 2013.