According to the television report, Trump does not want to once again sign a waiver - which he did on June 1 and which is up for renewal every six months - blocking implementation of a law passed by Congress in 1995 mandating that the embassy be moved.
The report comes just a day after Trump's vice-president Mike Pence stated that the President was "actively considering" how and when to move the USA embassy.
"While for the past 20 years, Congress and successive administrations have expressed a willingness to move our embassy, as we speak, President Donald Trump is actively considering when and how to move the American Embassy in Israel from Tel Aviv to Jerusalem", Pence said at an event celebrating the 70th anniversary of the United Nations vote on the Partition Plan.
"[Under the Trump administration, the USA will] always stand with Israel", Pence proclaimed, according to the Jerusalem Post. The Palestinians claim East Jerusalem as the capital of their future state, while Israel has declared the entire city as its capital.
During the 2016 presidential campaign, Trump vowed several times to move the USA embassy, which like other global missions is now located in Tel Aviv because of Jerusalem's disputed status.
Danon also addressed the event, saying that the United Nations vote paved the way for the creation of the Middle East's "beacon of democracy". "As President Trump says, 'If the world knows nothing else, let them know this: America stands with Israel'".
Israeli Transportation Minister Israel Katz, Israeli Ambassador to the UN Danny Danon and Ron Lauder, the president of the World Jewish Congress, will address the audience at the event, which was organized by the Israeli mission to the UN. "President Trump made this decision to maximize the chances of successfully negotiating a deal between Israel and the Palestinians, fulfilling his solemn obligation to defend America's national security interests".
He also commented on US efforts at the UN, repeating USA envoy to the UN Nikki Haley's words that "the days of Israel-bashing at the United Nations are over".
Pence's pledge comes days before the December 1 deadline for Trump to decide whether to waive a 1995 law mandating moving the embassy to Jerusalem, which sources say that Trump will not renew.
However, the vice president's assurance this week is a positive indication that Trump will shift the plans for the move back into gear.