Such a decision, which U.S. officials have said has not been finalized, would violate decades of U.S. policy not to take a stance on the fate of Jerusalem on the grounds that this was an issue Israelis and Palestinians should negotiate and decide.
If Trump made such a move, it could spark demonstrations or violence by Palestinians or by Muslims around the world, in part because of the sensitivity of the Jerusalem site known to Jews as the Temple Mount and to Muslims as Haram al-Sharif.
The site includes the al Aqsa Mosque, the third-holiest site in Islam, and the golden Dome of the Rock. It was also the site of an ancient Jewish temple, the holiest place in Judaism.
Israel seized East Jerusalem, which includes the area, during a 1967 war. However, the Waqf, a Muslim religious body, manages the Islamic sites within the compound.
A senior U.S. official told Reuters last week that Trump was likely to make the announcement on Jerusalem's being Israel's capital on Wednesday, though his adviser and son-in-law Jared Kushner on Sunday said no final decision had been made.
Kushner is leading Trump's efforts to restart long-stalled Israeli-Palestinian peace talks, efforts that so far have shown little progress.
The White House said it would not take any action on Monday on whether to move the U.S. embassy to Jerusalem from Tel Aviv, something that Trump had promised to do in his presidential campaign.
Trump is expected to sign the waiver, according to several U.S. officials. One U.S. official said Trump was likely to accompany the signing with an order for his aides to begin serious planning for an eventual embassy move, though it was unclear whether he would establish a strict timetable.
Two other U.S. officials said on condition of anonymity that news of the plan to recognize Jerusalem as Israel's capital had kicked up resistance from the State Department's Near Eastern Affairs bureau (NEA), which deals with the region.
"Senior (officials) in NEA and a number of ambassadors from the region expressed their deep concern about doing this," said one official, saying that the concerns focused on "security."
The State Department referred questions to the White House.
The White House did not immediately respond to requests for comment about the concerns of U.S. and foreign officials about the possibility of recognizing Jerusalem as Israel's capital.
A fourth U.S. official said the consensus U.S. intelligence estimate on U.S. recognition of Jerusalem as Israel's capital was that it would risk triggering a backlash against Israel, and also potentially against U.S. interests in the Middle East.
The core issues in the Israeli-Palestinian dispute include borders, the future of Jewish settlements in the West Bank, the fate of Palestinian refugees and the status of Jerusalem.
The Palestinians seek to establish an independent state in the Israeli-occupied West Bank, territory captured in the 1967 Middle East war and the Gaza Strip, which is controlled by Islamist Hamas, with East Jerusalem as its capital.
U.S. allies voiced their misgivings about the United States unilaterally calling Jerusalem Israel's capital.
"Any U.S. announcement on the status of Jerusalem prior to a final settlement would have a detrimental impact on the peace process and would heighten tensions in the region," Prince Khalid bin Salman, Saudi Arabia's ambassador to the United States, said in a statement.
French President Emmanuel Macron "expressed his concern over the possibility that the United States would unilaterally recognize Jerusalem as the capital of Israel" during a phone call with Trump on Monday, Macron's office said after the two leaders spoke by telephone.
And in an unusually detailed statement published by Jordan's official news agency Petra, Jordanian Foreign Minister Ayman Safadi was quoted as having warned U.S. Secretary of State Rex Tillerson against the move in a call on Sunday.
Safadi said such a move would "trigger anger across the Arab and Muslim world, fuel tension and jeopardize peace efforts," Petra reported.
The Palestine Liberation Organization's chief representative in Washington, Husam Zomlot, said a formal U.S. recognition of Jerusalem as the capital of Israel would be the "kiss of death" to the two-state solution to the Israeli-Palestinian conflict.
"Should such a step be taken it would have catastrophic consequences," Zomlot told Reuters.
A fifth U.S. official said concerns of Palestinian and other Arab leaders about endorsing Israel's claim to Jerusalem were being taken into account but no final decisions had been made.
Daniel Benjamin, a former U.S. counter-terrorism official now at Dartmouth University, had a simple message: "This is playing with fire."