The 32-year-old has just five months remaining on his current deal, but Arsenal and Ozil's representatives are discussing an early termination.
Ozil was excluded from Mikel Arteta's 25-man Premier League squad in October and dropped from Europa League consideration.
If the two parties can't come to a compromise, Ozil would reportedly see out the remainder of his contract and leave on his own accord when it expires on June 30.
The former Real Madrid midfielder said in a recent Twitter Q-and-A that he has no intention of retiring and aspires to play in Turkey and the United States.
"There are two countries I want to play football in before I retire: Turkey and USA. If I went to Turkey, I could only go to Fenerbahce," Ozil said.
"Every German-Turkish person supports a Turkish team when they grow up in Germany," he said. "And mine was Fenerbahce. Fenerbahce is like Real Madrid in Spain. The biggest club in the country."
Ozil hasn't featured in a competitive match since March 7.