The closed-door meeting is being convened as the majority of Republican Senators refused to call on US President Donald Trump to concede defeat in the presidential election, The Hill said.
After the meeting, Pence will reportedly leave for the southern island of Sanibel for a vacation.
Following a tight race in several key states, Democratic presidential nominee Joe Biden was projected as the winner of the election, securing more than the 270 electoral votes needed to take over the White House. Incumbent President Donald Trump disputes the calls made by most major networks, saying the election was far from over and he would take it to the courts to be resolved.
China, Brazil, Mexico, and Russia are among the nations that have so far not congratulated Biden on his projected victory in the US presidential race. On Monday, Kremlin spokesman Dmitry Peskov said that it was necessary to wait until the official results of the US presidential election are announced before congratulating Biden.