The phone call, which is the first time the pair has spoken since the vice presidential debate last year, was described by officials as “gracious and pleasant”, reports The New York Times.
It is the first and only interaction between the two campaigns since the November 2020 election, and the outgoing president has still refused to concede to Mr Biden.
Mr Pence and his wife, Karen Pence, may even entertain Ms Harris and her husband, Doug Emhoff, at the vice-president’s residence before Wednesday’s inauguration, said one official.
That plan may change depending on security arrangements as the week develops, reported theTimes.
While Mr Trump has largely stayed out of sight following the violence caused by his supporters, Mr Pence has attended a string of meetings and even met with National Guard troops now protecting the Capitol instead of the president.
Mr Trump, who was impeached for an unprecedented second time on Wednesday, is expected to leave the White House for a final time early on inauguration day and head for Florida.
The outgoing president reportedly hopes to leave Washington DC with a military band playing and a red carpet.
He will become the first president to snub his successor’s inauguration since the 1860s, but Mr Pence has said he expects to attend the event.
Traditionally, the outgoing president has met with the incoming first family at the White House before the inauguration.
The federal government will reportedly bring in outside contractors to carry out a $500,000 deep clean of the White House, which was the scene of multiple Covid outbreaks.
— Jonathan Martin (@jmartNYT) January 15, 2021
Mr Trump was impeached in the House for “incitement of insurrection” following the mayhem, and will be tried by the Senate after his departure from office.
The riot left five dead, including a US Capitol Police officer and a San Diego woman shot by law enforcement, as the pro-Trump mob tried to prevent lawmakers from certifying Mr Biden’s victory.
Police and the FBI have made a string of arrests in the wake of the violence, and Nancy Pelosi has announced a review of the Capitol’s security.