The Germany international attracted an approach from Arsenal last month, but decided to stay with Bayern.
However, he is on track to leave when his contract expires in June and BILD says Arsenal are one of several major giants keen on the midfielder.
AC Milan, Juventus, Atletico Madrid and Napoli are also interested, though the Gunners hold an advantage.
Goretzka, for his part, favours a move to the Premier League, where he is keen to test himself in the world's top competition.
Bayern’s sporting director Christoph Freund said last month: "Leon feels very much at home in this club and this team. Despite several quality inquiries, he has decided to stay here until the end of the season."
