Npower League One side Hartlepool claim they are owed more than £10,000 for ground improvements to Town’s home ground Befford Terrace. Pools currently use the ground for their reserve team fixtures.
If the court rules against Billingham, who play in the STL Northern League, they could be wound up.
Town committee member Peter Martin said: "We had hoped that Hartlepool United and their owners IOR may have dropped the case, but this does not seem to be the case.
"At the moment we are mustering as many grass-root supporters as we can to stand outside the court from 9.30am on the day wearing their football shirts in a stand of solidarity against one football club winding-up another.
"The consequences if we lose the case are that we cease trading, the team ceases to play football immediately and all the hard work of the volunteers, committee members and sponsors who contributed to build the ground up from nothing will be lost."
The case will be heard on Wednesday on the 27th October.