No date has been formally announced for the trip, but sources familiar with the planned visit said it could begin at the weekend.
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 U.S. Congress and the U.S.-Israeli relationship.
An Israeli official said Prime Minister Benjamin Netanyahu and other senior members of his cabinet held consultations on Wednesday on a "final decision" about the visit.
Denying entry to elected U.S. officials could further strain relations between Netanyahu, who has highlighted his close ties with U.S. 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.
Both House Majority leader Steny Hoyer and Minority leader Kevin McCarthy said in a pressconference in Jerusalem Sunday that Israel shouldn’t close the door on two freshmen Democratic congresswomen
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 lawmakersTemple Mount compound in Jerusalem that houses al-Aqsa mosque, A holy site for both Jews and Muslims, has turned into an issue of contention.
"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 would require Israeli security protection.
Violence erupted there on Sunday between Israeli police and Palestinians amid tensions over visits by Jewish pilgrims 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.
In February, Omar, 37, apologised after Democratic leaders condemned remarks she made about the pro-Israel lobby in the United States as using anti-Semitic stereotypes.