A key foreign policy adviser to Donald Trump is to meet the Israeli and Palestinian leaders as part of efforts by the White House to formulate a more coherent vision of how it will proceed with the Middle East peace process.

Jason Greenblatt, a Trump lawyer turned special envoy, was due to arrive in Israel on Monday for talks with the Israeli prime minister, Benjamin Netanyahu, and the Palestinian president, Mahmoud Abbas, on Tuesday.

Greenblatt’s visit follows a 20-minute telephone conversation between the US president and Abbas on Friday during which Abbas was invited to Washington to meet Trump.

The US president’s vision for peace in the Middle East, however, remains nebulous, with the White House saying on Friday after the Abbas conversation that “the president emphasised his personal belief that peace is possible and that the time has come to make a deal”.

Greenblatt – who like Trump’s pick for US ambassador to Israel, David Friedman, has no track record in diplomacy – was Trump’s chief legal officer dealing almost exclusively with real estate matters before being appointed as foreign policy adviser.

One of the key issues to be discussed is reportedly guidelines for Israeli settlement construction in the occupied Palestinian territories, which Greenblatt has said in the past he does not regard as an obstacle to peace, though he supports a two-state solution.

Greenblatt’s emergence as one of Trump’s key advisers on Israel last year also came as a surprise to the lawyer, who noted: “I knew that he was relying on me for certain aspects of Israel, but I didn’t know I was his top adviser,” he said responding to comments made by Trump.

Greenblatt and Trump. Photograph: Twitter

Trump has offered often confused and conflicting views on the Israeli-Palestinian question, both as candidate and president, including suggesting at a press conference with Netanyahu that he was not necessarily committed to a two-state solution.

Trump had also promised to controversially move the US embassy from Tel Aviv to Jerusalem on the first day of his administration, a move that has yet to materialise.

Palestinian officials, including Abbas in his conversation with Trump on Friday, have insisted they see the establishment of a Palestinian state alongside Israel as the only option for peace.

Before the visit – and amid signs that Trump might be turning his mind to the issue of a Middle East peace process in which he has promised to deliver the “ultimate deal” – Israel’s hardline defence minister, Avigdor Lieberman, intervened once again, calling for Israeli citizens of Palestinian origin to be transferred to any new Palestinian state including Israeli-Arab MPs.

Writing on his Facebook page on Monday, Lieberman said: “It cannot be that a hegemonic Palestinian state will be established, without a single Jew – 100% Palestinian, and Israel will be a binational state with 22% Palestinians.”

Commenting on several prominent Israeli Arab MPs, he added: “There is no reason that Sheikh Raed Salah, Ayman Odeh, Basel Ghattas or Haneen Zoabi will continue to be citizens of Israel.”

Greenblatt’s visit comes amid mounting questions over who is calling the shots in the Trump administration over its Middle East diplomacy.

While former President Barack Obama’s key negotiator was his secretary of state, John Kerry, Trump’s secretary of State, Rex Tillerson, has been almost invisible since taking office.

And while Trump has suggested that his son-in-law Jared Kushner – again lacking any track record in diplomatic negotiations – could take a lead in talks between Israelis and Palestinians, there has been little evidence of what Kushner’s vision is or what his real role might be.