The call was not listed on the prime minister's schedule or on the White House schedule, but Haaretz reported it was Trump who called Netanyahu after the US president spoke with Jordan's King Abdullah.
McMaster said Tuesday that Trump would not be accompanied by any Israeli leaders when he visits the Western Wall next week.
Israel captured the Old City and east Jerusalem in 1967 and later annexed it to the rest of the city - a move the global community does not recognize.
The President's Israel trip schedule: "The President will continue on to Jerusalem where he will meet with President (Reuven) Rivlin and lay a wreath at Yad Vashem".
Since Trump took office last month, Israel has announced plans to build over 6,000 settler homes in the West Bank and east Jerusalem - occupied territories claimed by the Palestinians.
Israeli officials were told by the White House that Prime Minister Benjamin Netanyahu could not join Trump because the wall is not a recognized Israeli territory.
Israel illegally annexed East Jerusalem after the 1967 occupation, and neither the U.S. nor much of anyone recognizes that as legitimate.
As president, Trump has said he'd like to try to broker a peace agreement between Israel and the Palestinians, calling it "the ultimate deal".
Israeli media outlet Walla! reported later that the White House tried to distance itself from the comments, saying that it did not reflect the position of the USA or of the President. His inner core of top advisors was populated with enthusiastic proponents of expanding Israeli settlements in the West Bank and, in a highly-contested move, the president appointed a very partisan David Friedman as ambassador to Israel.
The former bankruptcy lawyer has expressed scepticism over the two-state solution to the Israeli-Palestinian conflict, the basis of years of U.S. peace efforts.
"For violence to occur there could be any reason or no reason and if we, God forbid, because of fear of violence wouldn't do the right things, there would never be Israel, there would never be a reunited city", Barkat said.
"It would advance it by fixing a historic wrong and shatter the Palestinian illusion that Jerusalem is not the capital of Israel".
Bennett said he was not sure why Trump has changed his rhetoric.
Just another day at the Western Wall.
Trump has two weeks to make that decision, before the embassy automatically moves based on a 1995 USA law mandating the location switch.
Another issue that has come up in advance of Mr. Trump's visit is the USA embassy - during his presidential campaign, he promised to move the us embassy from Tel Aviv to Jerusalem, though he's been less vocal about it since taking office.
The rival claims to east Jerusalem lie at the heart of the Israeli-Palestinian conflict.