Flake, who did not seek re-election in 2018, frequently tangled with Trump and often said he hoped a Republican would challenge Trump in 2020. Flake told "CBS This Morning" on Tuesday "that somebody won't be me. I will not be a candidate."
Flake retired this month and is now a CBS News contributor. He says that it's "a difficult path" for any Republican to challenge Trump in a primary but that he still hopes someone will do so.
Flake was a U.S. senator from Arizona from 2013 to 2019. Previously, he represented Arizona's 6th Congressional District in the House.