Corker, 63, who serves as chairman of the powerful Senate Foreign Relations Committee, has in recent years become a central figure in policy negotiations with the Obama administration, including on the U.S.-Iran nuclear deal. He previously served as mayor of Chattanooga, Tenn.

The Trump campaign would not comment. Corker’s spokesperson did not respond to multiple requests seeking comment.

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Monday’s meeting comes weeks after Corker praised Trump’s late April address on world affairs. The people close to Trump said he has told friends that he deeply appreciated the effusive support from Corker, especially at a time when others in the party were sharply critical.

Ever since, Trump and Corker have remained in touch and they are said to have a friendly rapport. Both men consider themselves to be deal-makers and Republican mavericks. And both come from the world of real estate — Corker, one of the wealthiest members of Congress, has made millions of dollars on construction projects, investments and various properties.

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As a Senate Republican insider and establishment figure who sees Trump as a welcome addition to the GOP, Corker could fit part of the informal criteria that Trump has laid out as he thinks through his options.

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In an April interview with The Washington Post, Trump said that he would not pick an outsider like himself as his vice-presidential nominee, but rather, “somebody that can walk into the Senate and who’s been friendly with these guys for 25 years, and people for 25 years. And can get things done. So I would 95 percent see myself picking a political person as opposed to somebody from the outside.”

Last week, Bloomberg News’s Josh Rogin reported that Trump campaign Chairman Paul Manafort has also been corresponding with Corker in a “series of phone calls” and that “Corker’s office is supplying information to the campaign.”

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Trump’s aides, who have been mum about the candidate’s short list, have tapped attorney A.B. Culvahouse Jr. to assist with the vetting process. His involvement, which was first reported by Bloomberg, is part of the campaign’s ramping up of the selection process. Culvahouse, a longtime GOP player, was involved with Sen. John McCain’s vetting of then-Alaska Gov. Sarah Palin in 2008.

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Beyond the vice-presidential speculation, Corker’s visit to Manhattan represents the latest in a string of huddles that Trump has had with prominent foreign policy voices in the Republican Party, in particular those who are not traditional conservative hawks with ties to the George W. Bush administration.

Trump met on Wednesday with former secretary of state Henry Kissinger, who served presidents Richard Nixon and Gerald R. Ford, and last week he met with former secretary of state James A. Baker III, who served George H.W. Bush.

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“What I heard in that speech was a candidate trying to espouse views not unlike Bush 41 and Jim Baker,” Corker told reporters this month, according to Bloomberg. “I heard some realism creeping back into foreign policy.”

The University of Virginia’s Center for Politics, in a Thursday analysis of Trump’s vice-presidential prospects, said that Corker would bring “serious foreign policy cachet,” but he “might not be flashy enough for Trump.”