It is understood the club and Barton's representatives are discussing a severance package which could see the midfielder officially end an ill-fated spell in Scottish football.
The 34-year-old briefly returned to Rangers' training ground last Thursday after being suspended in September, but he has not been spotted since amid reports he has been signed off on medical grounds.
Barton was initially sent home days after a training-ground row in the wake of Rangers' 5-1 defeat at Celtic Park on September 10
The club announced his suspension the following week, which was later extended after the former Manchester City, Newcastle and QPR player was charged with breaching Scottish Football Association betting rules
The club had announced the end of a disciplinary procedure last Wednesday and Barton was told he would be returning to full-time training last week but he had to join the under-20s squad and was kept away from the first team
The former England cap faces an SFA hearing on November 17 but is unlikely to receive a lengthy playing ban given previous punishments issued to players who broke zero-tolerance rules which forbid gambling on any football match in the world.
With disciplinary options apparently limited, Rangers could pay up Barton's reputed Â£20,000-a-week contract until January, allowing him to train with a new club before signing when the transfer window opens.
Burnley manager Sean Dyche has refused to rule out a return to Turf Moor for the Liverpudlian, who turned down a new Clarets deal in the summer to sign a two-year contract at Ibrox.
Meanwhile, the official Rangers fans' group has become the club's fifth largest shareholder after buying almost 200,000 shares.
Club 1872 announced the purchase, which gives it a 6.25 per cent stake in Rangers International Football Club PLC.
Source : PA