No date has been formally announced for the trip, but sources familiar with the planned visit said it could begin at the weekend, Reuters reported.
Tlaib and Omar, the first two Muslim women elected to Congress and a flank of the Democratic party's progressive wing, have voiced support for the pro-Palestinian Boycott, Divestment, Sanctions (BDS) movement.
Under Israeli law, backers of the movement can be denied entry to Israel. But Israel's ambassador in the United States, Ron Dermer, said last month they would be let in, out of respect for the US Congress and the US-Israeli relationship.
An Israeli official said Prime Minister Benjamin Netanyahu and other senior members of his cabinet held consultations Wednesday on a "final decision" about the visit.
Denying entry to elected US officials could further strain relations between Netanyahu, who has highlighted his close ties with US President Donald Trump in his current re-election campaign, and the Democratic leadership in Congress.
"The possibility exists that Israel will not allow the visit in its current form. Professional and legal teams in the government ministries are continuing to examine the material," the official said.
Approval of the trip is still pending in the House of Representatives Ethics Committee, which would examine its itinerary, according to sources involved in planning the visit.
A planned tour by the two lawmakers of the holy compound in Jerusalem al-Quds that houses al-Aqsa mosque, and which is revered by Jews as the site of two biblical Jewish temples, has turned into an issue of contention.
The flashpoint site is in an area of Jerusalem al-Quds that Israel captured along with the West Bank in the 1967 Mideast War and annexed in a move not recognized internationally.
"To make sure there's apparent Israeli sovereignty over the site, they'll demand Israeli police go in with them, and not just the Waqf officials," said one of the sources with knowledge of the planned visit, referring to Muslim religious authorities.
An official in Israel's internal security ministry said any visit by Tlaib and Omar to the complex, revered by Muslims as the Noble Sanctuary and by Jews as the Temple Mount, would require Israeli security protection.
Violence erupted there Sunday between Israeli police and Palestinians amid tensions over visits by Jewish extremists on a day when the Muslim holiday of Eid al-Adha and the Jewish fast day of Tisha B'Av overlapped.
Tlaib, 43, who was born in the United States, draws her roots to the Palestinian village of Beit Ur Al-Fauqa in the West Bank. Her grandmother and extended family live in the village.
Ilhan Omar, who immigrated to the United States from Somalia as a child, represents Minnesota's fifth congressional district.