Gotze wrote his name into the history books at the last World Cup in Brazil as he scored an extra-time winner to fire Germany past Argentina.
The last four years have not been kind to the German attacking midfielder, however, and he believes a move to England could help to revive his career, according to the Daily Mirror.
Gotzes emotional return to Borussia Dortmund from Bayern Munich in 2016 has not gone well – he has contributed just four goals in two seasons for the Bundesliga outfit.
A worrying dip in form saw Gotze, 26, left out of Joachim Lows squad for this summers World Cup in Russia.
Premier League clubs have not been put off by Gotzes struggles, however, and the Mirror say Arsenal face competition from Everton and West Ham to secure his signature.
Low admitted it was a difficult decision to leave Gotze out of his World Cup squad – four years after his heroics in Rio – and said he hopes he can rediscover his top form soon.
If a player scores the decisive goal in the final at such a young age, it can be a burden later, the German boss said.
This season was not what we have all wished for from Mario Gotze. He just did not have the form. Its a difficult decision but I hope he returns.
Arsenal have made defensive signings their priority in Unai Emerys first transfer window since joining the club and landed Stephan Lichtsteiner from Juventus earlier in the month.
The Gunners are working on a deal for the Borussia defender Sokratis Papastathopoulos and have also made an approach to Chelsea for Brazilian star David Luiz.
According to reports, Chelsea have rejected a £17.6m offer from Arsenal, with the north London club now considering returning with an improved bid.