The youngster has shown impressive form in the Bundesliga, and is also reportedly attracting interest from Italian giants Juventus.
Arnold has featured for Germany at Under-21 level, despite being just 19 years of age.
He is under contract with Wolfsburg until 2015, and has a reported buy-out-clause of £8million.
He has featured for his country at every age-group level from Under-16’s, up to the Under-21’s, and is tipped to be a future star for the senior side.
Arsene Wenger smashed the club’s transfer record last summer to bring in German star Mesut Ozil from Real Madrid for £42.5million.
With Per Mertesacker, Lukas Podolski and Serge Gnabry already at the club, the Gunners appear to be building something of a German contingent.
The club were heavily linked with a move for Schalke star Julian Draxler in January, with club officials flying to Germany to try and negotiate a deal.
However, Wenger was thought to be reluctant to meet the £37million asking price, and decided against completing the deal.
Reports have suggested Arsenal may return for Draxler in the summer, but Wenger could turn to Arnold who would be a much cheaper alternative.