The four people briefed on the discussions requested anonymity because they were not authorised to speak publicly.
The lawyers who have spoken to the White House and are widely seen as the finalists are Marc Kasowitz; Robert Giuffra; Reid Weingarten; and Theodore Olson, the people said.
Two other lawyers who were originally viewed as contenders but have since drifted away from the mix, at least momentarily, because of various legal or professional obstacles are Brendan Sullivan of Williams & Connolly and A.B. Culvahouse, a partner at O'Melveny & Myers who is known for vetting political candidates.
Kasowitz, who has known Trump for decades, is expected to take a leading role. A partner at Kasowitz, Benson, Torres & Friedman in New York, Kasowitz has represented Trump in numerous cases, including on his divorce records, real estate transactions and allegations of fraud at Trump University.
Giuffra, Olson and Weingarten have already spoken to senior Administration officials about the team, said a person familiar with the process.
Giuffra, a partner at Sullivan & Cromwell in New York, is the coordinating counsel for Volkswagen, which has admitted to cheating on emissions tests in the United States.
Olson, a former U.S. Solicitor General, rose to prominence in 2000 when he argued the Supreme Court election case that delivered electoral victory to George W. Bush. He later teamed up with his former Democratic adversary on the Bush vs Gore case, David Boies, to successfully overturn the 2008 California ballot measure outlawing same-sex marriage.
Olson's late wife, Barbara, was killed in the September 11 terrorist attacks when the plane she was on crashed into the Pentagon. Olson, a partner at Gibson, Dunn & Crutcher's Washington, DC, office, is now married to Lady Booth Olson, a self-proclaimed lifelong Democrat.
Weingarten, a high-powered lawyer at Steptoe & Johnson in Washington known for his folksy style, is a somewhat unlikely choice because he has represented a series of Democratic clients, and is close friends with Eric Holder, who served as Attorney-General under former President Barack Obama. Holder and Weingarten met during their early years at the Department of Justice.
The four finalists did not immediately respond to requests for comment. A White House official said the Administration had no comment at this time.
Michael Cohen, a longtime lawyer for Trump and an executive at the Trump Organisation, remains the President's personal lawyer and confidant, and also is involved in the discussions, the people said.
The outside legal team would be separate from the White House Counsel's Office, which is led by Donald McGahn, who served as the Trump campaign's lawyer. In past administrations, presidents such as Bill Clinton have named outside counsel to help them navigate thorny legal problems.
Trump's push to put together an outside legal team comes as Robert Mueller, a respected former federal prosecutor and FBI director, begins his work as a Justice Department-appointed special counsel on the possible ties between the Trump campaign and Russian officials.
Controversy and political drama swirling around the alleged Russia ties have engulfed Trump's presidency from the start, fueling anger within a White House that feels under siege and unfairly scrutinised. That feeling, in part, drove the president to fire James Comey, the FBI Director, and fallout from that decision led Justice officials to tap Mueller as special counsel.
Comey, who has agreed to testify before the Senate Intelligence Committee in an open session, has told friends that he took contemporaneous notes of his exchanges this year with Trump. Democrats have seized on those news reports as evidence of potential obstruction of justice, with some Trump critics suggesting that impeachment could eventually be a possibility.
