As the leagues immediately below the BSN have set out their fixtures for the upcoming season, it leaves Celtic with the possibility of having no league to play in unless their appeal is successful.
They are hoping that a precedent set last summer will save them. The Football Association blocked attempts to remove Northwich Victoria from the same division.
"They seem to be completely disregarding the precedent that has been set." said a club spokesman Philip Morris.
"We shall be immediately launching an appeal, and beginning a fund to raise sufficient money to pay the fees to do so.
"If the FA uphold the Conference's decision, with the fixtures arranged for the next season throughout the non league pyramid Farsley Celtic basically will have no league in which to play."