The 25th Amendment was still under consideration in case the president becomes more volatile in his final days in office, a source close to Mr Pence told CNN.
However, there is concern that the use of the amendment or the impeachment may encourage Mr. Trump to act recklessly, thus putting the nation at even greater risk, the source added.
The 25th amendment states that the vice president would take over if a sitting president is removed from office, resigns or dies while in office. Invocation of the amendment requires the approval of the Vice-President and the majority of the President’s cabinet.
Tensions had mounted between Mr. Pence and Mr. Trump in the days leading up to the U.S. Capitol riots. The president had lobbied for Mr. Pence to challenge electoral certification in Congress, despite the Constitution granting no power to the vice president to do so.
At his “Stop Theft” rally on Wednesday, Mr Trump said he would be “very disappointed” with his vice president if he did not act. According to reports, the president never spoke to Mr. Pence during the riots that followed on the United States Capitol.
The couple have not spoken since the violence on Capitol Hill, CNN reports. Five people, including a Capitol police officer, died in the riots.
Mr. Trump has not publicly condemned the death threats on social media against his vice president. The White House issued a statement on Saturday saying it “strongly condemns all calls for violence, including those against any member of this administration.”
One of the last tweets Mr. Trump sent, before his account was permanently deleted by Twitter, was to announce that he would not be attending Mr. Biden’s inauguration.
Meanwhile, an assistant to the vice president said Mr Pence would attend the inauguration on January 20, Le New York Times reports.
Last week, Mr Biden said he was happy not to see Mr Trump attend his inauguration given everything that has transpired on the U.S. Capitol. But he added that Mr Pence was “welcome” at the event and that the presence of the vice president would help the transition process.