Minister says president will get the honor after "historic" recognition of Jerusalem as Israel's capital.
The State Department has refused, but Trump will have the final say on the matter.
Despite widespread criticism from abroad, Israeli Prime Minister Benjamin Netanyahu vowed "there will be others" moving embassies to Jerusalem.
The graffiti is a reference to the president's decision to move the U.S. embassy to the contested city.
Allies of the president's son-in-law, Jared Kushner, apparently don't think this spells an end to the peace process.
The U.S. president's thinking has been shaped and informed largely by these three men.
"If you are a broker, you do not want to kiss one side and kick the other," Ahmad Tibi tells Newsweek.
The State Department will make an official announcement as early as Tuesday, according to several sources familiar with the matter.
"It's a very serious issue with respect to the harm that certain individuals have suffered," Secretary of State Rex Tillerson told CBS.
After Vladimir Putin's instructions, Moscow is preparing a lawsuit on consulate closure, Russia's deputy foreign minister says.
Washington has closed a handful of diplomatic annexes and compounds.
Russia's foreign ministry has summoned a U.S. diplomat in Moscow to hand a formal note of protest.
The West needs to keep diplomatic, economic and cultural relations with Russia, but it must be wary of embassies becoming nests for hostile intelligence activity.
The holy site is a dangerous weapon in the hands of extremists and political Islam.
Israel says metal detectors will remain at the contested site.
McMaster, Tillerson, Mattis, and Kelly have largely ruined their own credibility.
Trump shouldn't even try to get the Israelis and Palestinians to the negotiating table.
A tweet from the embassy comes days after a report that suggested Rich was a WikiLeaks informant, which has since been refuted.
The WikiLeaks founder will stay in the embassy until the U.K. clarifies whether it has received an extradition request from the U.S., his attorney tells Newsweek.