White House officials believe the President has the backing of Republican allies in Congress and that impeachment is not in the cards, according to the people briefed on the legal discussions.
Even Democrats have tried to calm impeachment talk out of concern as it is premature.
But lawyers in the White House counsel's office have consulted experts in impeachment during the past week and have begun collecting information on how such proceedings would work, a person briefed on the matter told CNN on Friday.
However, a White House official denied the report saying "it's not true" that the lawyers are researching impeachment procedures.
The legal discussions are part of a broader internal effort to bolster the President's legal defence, which has become more complicated with the Justice Department's appointment of a special counsel to pursue the investigation into Russian meddling in the 2016 election.
Earlier this week, close advisers to the President, including lawyer and surrogate Michael Cohen, visited the White House to discuss his need to hire personal attorneys for Mr Trump.
If an impeachment hearing was opened with the majority of votes at the House of Representatives, it would then require at least two thirds of the votes at the Senate, which is still controlled by a conservative majority, reports Efe news.
Only three US presidents have ever faced impeachment or imminent threats of impeachment.
Former Presidents Andrew Johnson and Bill Clinton were impeached but later acquitted, while Richard Nixon resigned from office in 1974 before impeachment proceedings could begin.