The 19-year-old joined the Ibrox outfit in January after spending the previous year on loan with Sheffield United, making nine appearances for Walter Smith's side.
The Arsenal youngster's time in Scotland was cut short after he sustained a season-ending knee ligament injury in a Europa League tie against PSV Eindhoven in March.
However, Bartley - who has made one Champions League outing for the Gunners against Olympiakos in December 2009 - was back in Glasgow on Sunday to celebrate the team's SPL title victory, hoping that a deal to bring him back up north from Emirates Stadium could be on the cards.
Departing Rangers boss Smith has already talked to Arsenal supremo Arsene Wenger about a possible deal for next season, and it seems that Bartley is just as keen.
"There are talks going on with Arsenal as we speak so we'll have to wait and see but if I'm told I can come back that would be fantastic," he told Rangers' official website.
"The experience this year was invaluable and I really enjoyed my time so if I could some back next season that would be fantastic.
"All the boys get on really well and they're all great lads and now they can celebrate this success together."
By Colin O'Hanlon
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
‘Ruben Amorim could have waited for Real Madrid and had a better chance to be successful – to have joined Manchester United, he must be convinced in his own ability’ Former Old Trafford coach’s verdict on new boss
