Managed by Terry Butcher, the Edinburgh club were seventh in the 12-team table in November at the time of the former England international's appointment but have endured a torrid time since.
Hibs are without a win in their last 13 league matches dating back to Feb. 15.
Relegation would cap a miserable season for football in Edinburgh with rivals Hearts, who suffered a 15-point deduction after entering administration in January, already relegated to the second tier.
(Reporting by Tom Hayward; editing by Justin Palmer)
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