The German international, 31, will depart Bayern Munich at the end of the season after deciding to see out his contract. Arsenal explored a deal in January but Goretzka chose to remain in Munich for loyalty reasons.
While Italian clubs including Inter Milan, AC Milan and Juventus are also interested, Goretzka reportedly prefers a move to the Premier League. The experienced midfielder, who has played 21 Bundesliga appearances this season scoring twice, would add Champions League experience to Arsenal's midfield.