"I think we're gonna make progress", Friedman said in an interview Fox News host Jeanine Pirro, only one day ahead of the widely-anticipated United States embassy relocation from Tel Aviv to Jerusalem.
Mr Trump has been criticised for handing his ally, Israeli Prime Minister Benjamin Netanyahu, a political victory without insisting on any Israeli concessions that might mollify Palestinians and help revive the moribund peace process.
"Under any peace agreement [with the Palestinians] Jerusalem will remain the capital of Israel", Netanyahu said.
Speculation has surfaced in the Israeli media that Mr Trump is planning a counter to the embassy move, requesting that Israel withdraw from four East Jerusalem neighbourhoods.
Rick Scott is visiting Israel and will be on hand for the opening of the USA embassy in Jerusalem.
Netanyahu on Sunday praised Trump's "bold decision" in upending decades of US policy by relocating the embassy from Tel Aviv and recognizing Jerusalem as Israel's capital.More news: China's first domestically built aircraft carrier begins maiden sea trial
Ismail Haniyeh, head of the Islamic Resistance Movement.
Observers say there is concern that expanding Palestinian protests may lead to clashes with Israeli forces. Forty protesters have been killed and more than 1,700 wounded by Israeli troops since late March. It will also be given to all world leaders who move their embassies to Jerusalem and was recently bestowed on Guatemalan President Jimmy Morales.
Their dismissal of Mr Trump's unilateral action last week has shown that the worldwide community is now willing to say "no" to the United States, the sole global superpower, said Mr Shaath.
It was not immediately clear from Ambassador David Friedman's remarks, on a call with reporters, whether Mr Trump will speak via a live videolink or a pre-recorded address. Under the law, presidents could delay the move by signing a waiver every six months, which Presidents Clinton, Bush, Barack Obama and Trump did until December. The new embassy is due to open on Monday. Previous recipients of the award are also President George W. Bush, Prince Albert II of Monaco, President Rosen Plevneliev of Bulgaria and recently also President Jimmy Morales of Guatemala, for declaring he will move the embassy to Jerusalem. "Today's move of the USA embassy gives life to a religious conflict instead of a dignified peace". Nethanyahu praised President Trump's "bold decision" to move the embassy to contested Jerusalem.
Ivanka Trump and her husband Jared Kushner as well as Treasury Secretary Steven Mnuchin are scheduled to attend the opening ceremony on Monday, which coincides with the 70th anniversary of the founding of Israel.
He tells ABC's "This week" that "if you're not prepared to recognize that Jerusalem is the capital of Israel and that's where the American Embassy should be, then you're operating on a completely different wavelength". He sent a statement ahead of Monday's ceremony that called the move illegal and an obstacle to "a just and lasting peace between two sovereign and democratic states".