Trump's VP list shrinks
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Donald Trump's vice presidential options are shrinking now that he’s lost Sen. Bob CorkerRobert (Bob) Phillips CorkerPollster says Trump unlikely to face 'significant' primary challenge GOP gets used to saying 'no' to Trump Democrats introduce bill to rein in Trump on tariffs MORE as a potential running mate. 

The presumptive GOP nominee also appears to be losing freshman Sen. Joni Ernst (Iowa), who, according to multiple reports, would rather remain in the Senate. 

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Speculation has recently swirled around the two Republican senators as the time for Trump to decide on a running mate draws closer.

Corker, chairman of the Senate Foreign Relations Committee, took his name out of the running on Wednesday, a day after campaigning with Trump in the battleground state of North Carolina. It was at this campaign appearance where Trump praised former Iraqi dictator Saddam Hussein.

Corker did not reference Trump's comments when he told The Washington Post he was pulling out of consideration. 

“It’s a highly political job, and that’s not who I am,” Corker said. 

The Tennessee Republican has recently been warming up to Trump and in May offered to advise Trump on foreign policy at the real estate mogul’s request.

Asked whether Trump offered him a position in his Cabinet, Corker, who noted they had a "wide-ranging conversation," said the campaign wasn't there yet. 

"The two things in front of them are getting a vice president and, secondly, making sure the convention goes off," he told reporters on Wednesday. "It's a really lean campaign, I mean very lean, so that's their focus right now." 

Now Ernst is also reportedly withdrawing her name from consideration. She told Politico in an interview Wednesday that she plans to help Trump’s campaign but wants to continue as a senator.

Ernst’s office would not comment on her status as a vice presidential contender but pointed to the Politico report that said she had "all but" withdrawn.

“I made that very clear to him that I’m focused on Iowa. I feel that I have a lot more to do in the United States Senate. And Iowa is where my heart is,” Ernst said. “And I think that President TrumpDonald John TrumpThorny part of obstruction of justice is proving intent, that's a job for Congress Obama condemns attacks in Sri Lanka as 'an attack on humanity' Schiff rips Conway's 'display of alternative facts' on Russian election interference MORE will need some great assistance in the United States Senate, and I can provide that.” 

Cedar Rapids, Iowa, TV station KCRG reported that it had confirmed with Ernst's staff that she wants stay in the Senate.

The Iowa Republican had met with Trump on Monday and said they had a “good conversation.” 

Ernst is a popular lawmaker who defeated then-Rep. Bruce BraleyBruce Lowell BraleyOPINION | Tax reform, not Trump-McConnell feuds, will make 2018 a win for GOP Ten years later, House Dems reunite and look forward Trump: Ernst wanted 'more seasoning' before entertaining VP offer MORE (D) in one of the most watched Senate races of the 2014 cycle. 

While she said she would likely be involved with Trump's campaign as “an advocate,” Ernst has been critical of the candidate in the past. She has criticized his inflammatory remarks about women earlier this year and said they could hurt him among female voters.

Trump has said he will announce his running mate at the Republican National Convention in Cleveland, which begins July 18, though CNN reported on Tuesday that he would likely announce his decision next week

On Wednesday afternoon, Trump said in an interview on Fox News that he’s “looking at 10 people” who could be his running mate.

At the top of the list are New Jersey Gov. Chris Christie and former House Speaker Newt Gingrich (Ga.). 

Christie, who was one of the first high-profile Republicans to rally behind Trump when it appeared he would be the GOP nominee, is on vacation with his wife in Italy for a few days. 

Gingrich will reportedly campaign with Trump in Cincinnati on Wednesday night. 

The real estate mogul said in Wednesday's Fox News interview that two generals are currently being considered. But he noted that he is more inclined to pick a lawmaker. 

"I like the generals; I like the concept of the generals,” Trump said, “[But] we're looking to go more the political route in terms of getting legislation passed." 

Other possible candidates mentioned over the past several weeks include Indiana Gov. Mike Pence, Alabama Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsThe Memo: Mueller's depictions will fuel Trump angst Collins: Mueller report includes 'an unflattering portrayal' of Trump Trump frustrated with aides who talked to Mueller MORE, Oklahoma Gov. Mary Fallin, Tennessee Rep. Marsha BlackburnMarsha BlackburnConservative groups defend tech from GOP crackdown Lawmakers weigh challenges in fighting robocalls Senators show deep skepticism on Space Force proposal MORE, retired neurosurgeon Ben Carson, former Massachusetts Sen. Scott Brown and Ohio Gov. John Kasich. 

Trump’s vice presidential pick could be a crucial moment for his campaign and the Republican Party as they seek to become a united front going into the general election against presumptive Democratic nominee Hillary ClintonHillary Diane Rodham ClintonThorny part of obstruction of justice is proving intent, that's a job for Congress Nadler: I don't understand why Mueller didn't charge Donald Trump Jr., others in Trump Tower meeting Kellyanne Conway: Mueller didn't need to use the word 'exoneration' in report MORE, who has hit the ground running with a much larger staff and campaign bank account.

Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSenate Republicans tested on Trump support after Mueller Anti-smoking advocates question industry motives for backing higher purchasing age Former Bush assistant: Mueller report makes Obama look 'just plain bad' MORE, who has endorsed Trump, has been critical of Trump recently and called on him to “get on message.” 

The Kentucky Republican sidestepped weighing in on whom Trump should pick amid speculation that multiple members of his caucus could be under consideration.

"I have no idea who we'll pick," he told reporters. "We're all obviously quite interested."

Jordain Carney contributed