It also referred to an Egyptian-led resolution at the United Nations last month that rejected USA recognition of Jerusalem as Israel's capital.
The visit was originally scheduled for December but it was postponed so the vice president could attend a Senate vote on Trump's tax overhaul plan.
The newspaper said in a report published Saturday that it obtained audio recordings in which an Egyptian intelligence officer, speaking with influential talk show hosts, asked them to downplay the significance of US President Donald Trump's decision.
"At President Trump's direction, the vice president is traveling to the Middle East to reaffirm our commitment to work with the U.S.'s allies in the region to defeat radicalism that threatens future generations", Pence spokesperson Alyssa Farah said in a statement.
She said Pence was looking forward to discussing with the leaders there ways to work together to fight terrorism and improve national security.
Egyptian religious leaders close to the government refused to meet US Vice-President Mike Pence.
Outwardly, Egypt has maintained a strict policy of condemning Trump's bombshell decision, which sent shock waves throughout the Middle East, sparking protests and violence.
The global community does not recognise Israeli sovereignty over the full city. Palestinian Authority President Mahmoud Abbas will not meet with the United States official in protest of the administration's move on Jerusalem.
Pence's agenda in Israel includes meetings with Prime Minister Benjamin Netanyahu and President Reuven Rivlin, an address to the Knesset and visits to the Western Wall and the Yad Vashem Holocaust memorial.
Jerusalem's status has always been one of the main obstacles to a peace agreement between Israel and the Palestinians. The Times article said that according to tapes of conversations between Kholi and four different hosts, the officer suggested that Palestinians should be content with Ramallah rather than east Jerusalem. Sissi will meet with Pence despite the deep unpopularity of Trump's decision.
The approach has pushed back against an global consensus that Jerusalem's status should be decided in negotiations between Israel and the Palestinians and comes as Trump has vowed to press forward with plans to help broker peace between Israel and the Palestinians.
"Hassaseen denied that he received such a phone call on Jerusalem, affirming that he does not know any man by the name of Ashraf al-Kholi", the statement said. The U.S. motion to recognize Jerusalem as Israel's capital was rejected by the U.N. Security Council and condemned by global leaders. Jordan has a large population of Palestinian origin, and the king serves as guardian of the third holiest site of Islam, located in east Jerusalem.More news: Firefighters respond to blaze at Trump Tower