BILD says with his contract expiring on June 30, a number of clubs are interested in the former Germany international.
West Ham and Everton are among those interested in the attacking midfielder, but will not match his current salary.
Gotze is believed to pocket around £170,000-a-week at Signal Iduna Park, but owing to his lack of recent form would have to take a pay cut to come to the Premier League.
It is thought that the former Bayern Munich attacker will have options in China, Qatar and Saudi Arabia - but would rather stay in one of Europe's top leagues.
AC Milan are also interested in capturing his signature.