Barkley, who first arrived at Hillsborough in early September, has made seven appearances for Dave Jones's side, scoring one goal. The 18-year-old had an outstanding first 45 minutes for the Owls in Friday night's 1-1 derby draw with Leeds.
"The boy still has academy status, so there's no timescale required on it, so we're lucky in one sense, but then Everton could call him back at a moment's notice if they get any injuries," Jones said.
"Ross has got better and better since he came here. The lad has a very bright future and playing games in the Championship will certainly help his development."
Meanwhile, the Owls have signed former Everton goalkeeper Adam Davies on a month-to-month contract.
The 20-year-old, released from Everton at the end of last season, will go straight into Jones's squad for Wednesday night's game at Blackburn as cover for Chris Kirkland as Stephen Bywater is sidelined with pneumonia and Arron Jameson is out for up to eight weeks with a recurrence of a groin injury.