Under the plan, Sen. Tom Cotton of Arkansas would take over for Pompeo at the helm of the CIA, the paper said in its online edition, quoting senior administration officials.
It was not immediately clear whether President Donald Trump has given final approval to the plan developed by his chief of staff John Kelly, according to the paper.
Asked by reporters about the matter at the start of his Oval Office meeting with the crown prince of Bahrain, Trump only said, "He's here. Rex is here."
Tillerson has been at odds with Trump's White House on a range of issues such as Iran, Qatar and most recently North Korea.
According to the report, Cotton, a Republican who has been a key ally of Trump on national security issues, has signaled that he would accept the CIA job if offered.
Under the plan, the shake-up of Trump's national security team would happen around the end of the year or shortly after, it said.
While some administration officials initially expected Tillerson to be replaced by U.S. Ambassador to the United Nations Nikki Haley, Pompeo has become the White House favorite.
Pompeo has impressed Trump during daily intelligence briefings and become a trusted policy adviser even on issues beyond the CIA's normal mandate such as health care, according to the paper.
The rift between the president and his chief diplomat came to light in early October following a news report that Tillerson was on the verge of resigning this past summer amid policy disputes with Trump.
It was also reported that Tillerson called Trump a "moron" after a July 20 meeting at the Department of Defense with members of Trump's national security team and Cabinet officials.
source: news.abs-cbn.com
