Arteta did not include the Spanish right-back in his team that beat Crystal Palace 2-0 in the Premier League opener last Friday.
Bellerin is now set to return to Real Betis, where he spent last season on loan.
This was confirmed by football transfer expert, Fabrizio Romano, on Tuesday.
“Héctor Bellerín’s agent is in London today as he met with Arsenal board, been told meeting took place in the morning. Discussions ongoing to terminate the contract.
“Bellerín asked to return to Real Betis as soon as possible, it’s his priority,” he said.
Bellerin will become the latest player under Arteta to have his contract terminated.
In January, Aubameyang left as a free agent to join Barcelona. Before him, Mesut Ozil had his deal torn up, before joining Fenerbahce.