Senator John Cornyn of Texas is one of at least 10 people under consideration by the White House to replace fired FBI Director James Comey.
Cornyn was one of several candidates interviewed on Friday at the Department of Justice.
Officials also spoke with acting FBI director Andrew McCabe, attorney Alice Fisher, federal Judge Henry Hudson and former Homeland Security Adviser Fran Townsend, according to CBS News.
"We can make a fast decision," President Trump said. "These are outstanding people that are very well known. They have been vetted over their lifetime essentially. Highly respected people and that's what we want for the FBI."
Cornyn's credentials include having served on the senate judiciary committee and as attorney general of Texas.
Whether Cornyn wants to give up his senate seat is unclear. He released a statement Friday saying:
"I have the distinct privilege of serving 28 million Texans in the US Senate, and that's where my focus remains."
If he is chosen as FBI Director, Texas Governor Greg Abbott would appoint someone to temporarily replace Cornyn in the senate.
Texas would eventually have to hold a special election to fill Cornyn's term which expires in 2021.