Prime Minister Benjamin Netanyahu early in November ordered the demolition of the family homes of Palestinians who carried out attacks on Israelis.
The attackers were all killed by security forces and the demolition orders have been denounced as collective punishment.
So far Israeli authorities carried out only one demolition, when they destroyed the flat of the Shaludi family on November 19, almost a month after Abdelrahman Shaludi deliberately ran over Israeli pedestrians in Jerusalem killing a young woman and a baby.
Police shot him dead at the scene.
The families of other attackers have appealed against the decision through Israeli rights group Hamoked, which told AFP the Supreme Court was to make a ruling on Wednesday.
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"We're not really optimistic since it seems like the Israeli public wants revenge, and the Israeli authorities want to show they still have power," Hamoked's director Dalia Kerstein said.
"The whole atmosphere smells like revenge," she said.
Five more homes are facing demolition, belonging to the families of east Jerusalem attackers who were all killed at the scene of their attacks against Jewish Israelis, apart from one who was killed in a raid on his house the following morning.
Rights groups have repeatedly condemned the practice, which had not been used in Jerusalem for more than five years prior to the recent orders, with some saying the demolitions will fuel further unrest.
The United States has also described the tactic as "counterproductive".
Tensions are running high in Jerusalem with near-daily clashes between Palestinians and police.
The unrest began in July when Jewish extremists killed a 16-year-old Palestinian in revenge for the murder of three Israeli teenagers in the West Bank.