The 19-year-old defender spent the last three months of the 2009/10 season on loan at Bramall Lane and was a regular for Kevin Blackwell's side, making 13 Championship appearances.
Bartley told Arsenal's official club website: "I'd obviously prefer to be in Arsenal's first team, but I'm realistic that it may not happen, I might have to wait a year or two yet.
"I've had a good couple of years in the reserve team and captained the side this year, which was a fantastic achievement.
"But maybe my next step will be to take another year out on loan and get some real competition under my belt. I'm open to different ideas really.
"I absolutely loved every minute of my time at Sheffield United. The facilities and the set-up are great there and all the lads are fantastic. I haven't got a bad word to say about them."