The Germany international met with Blaugrana representatives on Monday, according to Kicker.
Arsenal are looking set to automatically qualify for next season’s Champions League, but had things gone slightly different this season Arsene Wenger’s men could have been crowned English champions.
The Borussia Dortmund man is out of contract next summer, with growing speculation that his future may well be away from Signal Iduna Park.
The German newspaper have stated that the midfielder travelled to Camp Nou on Monday and held a meeting with Barcelona representatives as the respective groups look to thrash out a deal.
Barcelona are currently undergoing a transfer embargo and as such any new additions would not be allowed to join the club until January 2016.