"At the minute I don’t know what is going to happen," said Bartley, who came on as a sub in Arsenal’s friendly against New York Red Bulls on Sunday and scored an unfortunate own goal.
"The manager knows I want to play as much as possible but it’s completely up to him to decide what he thinks is best for my career.
"I really enjoyed my time at Rangers and we were very successful while I was there. It’s a fantastic club so of course I’d be happy to go back.
"But if the manager thinks it would be more beneficial for me to stay at Arsenal and learn here then I’ll take that chance too.
"I hope it will all be sorted out by the end of August but I just want to do what is best for me and for Arsenal."