Israelis allege the holy site is Jewish, calling it the Tomb of Patriarchs.
Saar instructed his ministry's Jerusalem district director to study the possibility of schools' agreement to take part in the project during the next academic year.
”It is very important that our students learn the historical roots of the land of Israel,” he said in press statements.
Jewish settler leader Noam Arnon said around 70,000 Jews heavily guarded by the Israeli army visit the mosque every year.
Israeli critics say the plan is designed to instill Jewish rightism in the youth and will be impractical requiring heavy security procedures.
Al-Khalil, which is under PA control, is home to more than 160,000 Palestinians against only 600 Jews who live in a quarter occupied by Israel.
The flashpoint city has been rife with clashes between the Palestinians and settlers backed by Israeli security forces. The army made a partial pullout in 1998.
The mosque is one of many Palestinian holy sites Israel has added to its Jewish heritage list.
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