Cornyn, 65, is the Senate majority whip and formerly served as a Texas attorney general and state supreme court justice.
Cornyn was among at least seven other candidates who interviewed with Justice Department officials about the position this weekend.
We reached out to Senator Cornyn's office about the interview.
The list is not a comprehensive accounting of finalists for the Federal Bureau of Investigation director positions.
"I think if Cornyn moves from Senator to FBI Director, that has a huge effect on our state politics", said University of Texas history professor Jeremi Suri. But Cornyn declined to say whether the Russian Federation probe or Comey's firing were discussed.
Cornyn had also been scheduled to deliver a commencement address on Saturday at the Texas Southern University in Houston, but university officials on Friday cancelled his appearance at the historically black college after a petition signed by hundreds of students protesting his appearance.
Interviews well underway for new Federal Bureau of Investigation director to replace Comey
Lindsey Graham said it is time for Trump to come clean about whether he recorded conversations at the White House. Senator John Cornyn, a former Texas attorney general, was also interviewed.
Several of those named could be considered outside shots: For example, while Thompson criticized Comey's handling of the Clinton emails, he also co-authored a Washington Post op-ed last October calling for Trump's electoral defeat. In recent days, the senator has maintained that his focus remains on his Senate seat, but his voting records and public statements of support have made him a close ally to Pres. Trump.
Republican Sen. Ted Cruz of Texas praised Cornyn saying he's supportive of the fellow Texas senator, but noting Americans need to be assured the position won't be politicized. On the Republican side, obvious potential candidates for appointment or election would be Lt. Gov. Dan Patrick, Land Commissioner George P. Bush and U.S. Rep. Michael McCaul, R-Austin, the chairman of the House Intelligence Committee who toyed with running against Sen. The former Republican senator from Alabama sharply criticized Cornyn's bipartisan effort a year ago to overhaul the nation's criminal justice system and revise some 1980s and '90s-era federal "tough on crime" laws.
The petition accused Cornyn, the No. 2 Republican in the Senate, of supporting "discriminatory policies and politicians", and argued that hosting him as a commencement speaker would contradict the university's values. In 2010, Cornyn led the committee to back Charlie Crist in the Florida Republican primary but then switched to Marco Rubio as the tea party favorite gained momentum.
The comment came Tuesday after Senate Majority Leader Mitch McConnell said he recommended that President Donald Trump nominate the federal appeals court judge for the post. Now more than ever the country needs a well-credentialed, independent FBI Director.
And if Patrick were to succeed Cornyn in Washington, the members of the Texas Senate would select his successor until a new lieutenant governor was elected in 2018.