The 19-year-old has shot to prominence at Signal Iduna Park with impressive displays for the Bundesliga champions, and he scored the winner recently in a 1-0 away victory over Bayern Munich.
Gotze has also broken into the Germany international setup, and is likely to play a part in Joachin Low’s first team at Euro 2012 in Poland and Ukraine.
Mirror Football state that Arsene Wenger is ready to bid £30 million for the playmaker come January, as a statement of intent to the likes of Robin van Persie to sign a new contract.
Dortmund have previously stated that Gotze was not for sale at any price, and have rejected rumours that he will leave Dortmund in the next transfer window.
Bayern Munich are also thought to be massively keen to add the attacking midfielder to their ranks, and if The Gunners do bid for the starlet they can expect competition from a number of leading European clubs.
By Gareth McKnight