The money was required by the League before granting Brighton permission to play in the Nationwide Third Division next season.
The League said in a statement that "with regret" the board of directors of the Nationwide Football League had called an extraordinary general meeting for the purpose of considering Brighton's expulsion from the League.
"They have not complied with the conditions laid down, and agreed by them, to ensure their continued membership," the statement read. "Specifically, they have failed to lodge the required bond with the League by the deadline of 20 June."
The club had planned to lodge the bond yesterday - seven days late - but have not met the League's approval and the showdown to decide their fate will be held on 24 July.
The League's threat will be welcomed in Hereford, the club relegated after drawing with Brighton on the season's last day.