The 20-year-old, who impressed in nine Light Blues games on loan last season before being struck down by a knee injury, is now hoping to get the news he wants next week.
Bartley told the Scottish Sun: "I'm still waiting to hear how Arsene feels about my situation. I've a long-term contract with Arsenal and I'll abide by whatever decision is made.
"But it's no secret I loved my time at Rangers - and they'd definitely be my first choice if my manager was to send me out on loan again.
"I have spoken to Ally several times since the end of the season and he has made it clear he'd like me to return.
"People are on holiday, but I'm hoping for an answer soon about where I'll be next season."