Petah Tikva were demoted after failing to raise the mandatory minimum 11.4 million shekels ($3.3 million) by last week's deadline and despite missing an extension on Tuesday when they said they did not have all the money.
That failure initiated a move by the Israeli FA to promote Hapoel Kfar Sava in place of Petah Tikva, who a day later declared they had made up the shortfall and would be able to present a viable budget.
The move prompted the FA's top court to agree to discuss the matter and make a final ruling on Sunday.
In a brief statement on Thursday, the Israeli FA said: "The supreme tribunal has decided that the hearing in the matter of Hapoel Petah Tikva and Hapoel Kfar Sava will take place this coming Sunday."
Petah Tikva finished third from bottom last season and won a relegation playoff against Kfar Sava who finished third from top in the second division.
As well as relegation, Petah Tikva were handed a nine-point deduction from the start of the new season.
Petah Tikva, one of two clubs from the central Israeli town near Tel Aviv, have suffered boardroom disputes recently.
They were a top side from the 1950s to the 1980s and won five consecutive league titles between 1959 and 1963, still a record.
The declared budgets for Israel's richest clubs for the coming season, which begins on Aug. 20, are about four times bigger than the required minimum. ($1 = 3.499 Israeli Shekels) (Writing by Ori Lewis; Editing by Ken Ferris; To; comment on this story email firstname.lastname@example.org; )