The R's are currently carrying out an internal investigation into Barton's actions during the last game of the season against Manchester City. The midfielder has already been suspended for 12 games and fined £75,000 by the Football Association for his behaviour at the Etihad Stadium.
Now, Rangers have now been informed by Moroccan international Taarabt that he is not happy to feature in the same team as Barton following two separate training ground incidents, according to the London Evening Standard.
It is believed that Taarabt has been left unhappy by two challenges that former England international Barton has made on him in recent weeks.
West Ham United have been credited with an interest in Barton.