Off contract at the end of the season, Goretzka is leaning towards leaving Bayern this summer.
BILD says several clubs are interested in the experienced midfielder.
AC Milan, Atletico Madrid and Arsenal are all keen and the 31-year-old Germany international wants to switch to the latter.
Goretzka revealed in late January that there is great interest in him.
"Although I am very honoured by the interest of international top clubs, I have made a clear decision for myself to stay with Bavaria until the end of the season," he said at the time.
"At the same time, the club and I have decided in good and constructive conversations that our successful time together will end this summer.
"As I have said before, it is also the right time for me to open a new chapter again – both as a football player and as a human being."