The four candidates will meet with Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein, the sources said. Comey was fired by President Donald Trump on Tuesday. Another name mentioned publicly is former House Intelligence Committee chairman Mike Rogers. He is not among those to be interviewed this weekend but sources say he could be included in a next round of meetings should the process continue. Cornyn, a former Texas Supreme Court justice and former Texas attorney general, issued a statement on Friday in which he said he remained focused on his constituents. "I have the distinct privilege of serving 28 million Texans in the United States Senate, and that is where my focus remains," Cornyn, who is majority whip in the Senate, said in the statement.

Acting FBI Director Andrew McCabe testifies before the Senate Intelligence Committee with the other heads of the U.S. intelligence agencies in the Hart Senate Office Building on Capitol Hill May 11, 2017 in Washington, DC. Getty Images