The North London club have met with officials from the German side to discuss the left-back.
The North London club have Nacho Monreal and Kieran Gibbs in the defensive position, but are ready to bolster their contingent ahead of next season.
The 20-year-old was a consistent performer for the Bundesliga side over last season, with the report also stating that Chelsea and Manchester City are keeping tabs on the defender.
The Ghana international started 29 of his side’s Bundesliga fixtures last season, with Bild stating that Arsenal met with representatives of the German club last week.
The Gunners finished last season strongly and will hope to start equally as well next term in a bid to put forward a consistent title challenge.
Rahman is under contract at Augsburg until 2019 but the German club are said to be in no position to fight off the financial power of some of England’s top clubs.
Bild state that a three-way stand-off for the player’s services is set to ensue, with the defender likely to leave his current employers ahead of the 2015-16 campaign.