Spanish publication 'Mundo Deportivo' claims that the Catalan side are confident of signing the player for just £17m in January, with the player's contract set to expire next summer.
The same source also reports that Ozil's agent, Dr Erkut Sogut, has already held talks with Pep Segura, Barca's general manager, making a deal more likely.
It is thought that Arsenal want to cash in on the German international in January, rather than see him leave the club on a free next summer.
That suits Barca, who are also keen on a January deal owing to Ozil's Champions League availability, with Arsenal only playing in the Europa League this season for the first time under Arsene Wenger, not that Ozil has featured in that competition anyway.
Ozil is thought to be Barca's number one alternative to Philippe Coutinho, who is widely expected to remain at Liverpool despite yet more reports linking him with a move to the Camp Nou.
The German was named Man of the Match in Saturday's north London derby as Arsenal eased past arch-rivals Tottenham 2-0, though it remains to be seen how popular he would be in Catalonia, owing to his Real Madrid past.