"I made that very clear to him that I'm focused on Iowa", she said, a few days after Trump suggested she might be on his list in a weekend tweet.
"It's a highly political job, and that's not who I am", Corker said.
Corker said he would be open to serving in a Trump administration and that his decision to take himself out of running for vice president opened up "a candid conversation" about other possibilities.
Unlike Ernst, who said Wednesday she had been given vetting papers by the Trump campaign, Corker had been formally considered, submitting documents to the attorney overseeing the process.
Former House speaker Newt Gingrich, New Jersey Gov. Chris Christie and Indiana Gov. Mike Pence remain near the top of the short list, according to multiple Trump campaign associates. Caputo, who resigned from the Trump campaign June 20, said people close to Trump are advocating for Pence.
"So, I'm going to move on", he told the Post. People across the country involved in Republican politics who found him to be a very personable man.
Later Wednesday, a Republican adviser confirmed to CNN that Ernst will be speaking at the convention on the topic of national security. "I view myself as deep in substance and policy and I just think there are better ways for me to serve the public and I cherish what I'm doing now". Asked if she got special treatment, Ryan said: "Looks like it to me".
Donald Trump doubled down on his controversial comments on Saddam Hussein last night, hours after two high-profile Republicans withdrew from vice presidential consideration yesterday. I think most people who know me agree with that.
Ernst, for her part, told Politico that she favors Pence, calling him "so well rounded" and "a great conservative".
Asked if he would consider working in a Trump administration, Corker said he shares the same philosophy of public service as Howard Baker Jr., a former Tennessee senator who served as President Reagan's last chief of staff and, later, as USA ambassador to Japan.
No other reported VP possibilities have much reputable foreign policy experience, and Trump's credibility on the issue is (justifiably) under attack.