The German international is out of contract at the end of the season, meaning that he can talk to overseas sides over a bosman move in January.
English publication 'The Daily Mail' reports that Arsenal are one of a number of sides monitoring Goretzka's situation and are set to launch a move in the New Year, with the club confident that they are in a strong position to land the midfielder.
Goretzka is thought to have attracked interest from a number of top European sides in the last 12 months with Barcelona, Manchester City and Juventus all having been linked with the player.
Arsenal have been working on expanding their knowledge of Germany after signing Sead Kolasinac on a free from Schalke last summer and are keen on adding 22-year-old Goretzka to their ranks.
The classy midfielder has scored four goals in nine Bundesliga games so far this season but is currently sidelined by a stress fracture.
Goretzka has also forced his way into the Germany set-up of late, scoring six goals in 12 games for 'Die Mannschaft.'
The midfielder is renowned for being good on the ball and given his stats he clearly has an eye for goal, meanwhile, at 6'2", he is also more than capable of adapting to the rigours of Premier League football.
Would he be a good signing for Arsenal?