He did not, however, break out his catchphrase "You're hired!"
The Republican front-runner then said he "felt good about her" and that his "gut instinct" told him that she would be a good hire.
The woman showed her gratitude by giving him a hug and kiss on the cheek.
Trump said he would soon unveil more people who are helping him shape his foreign policies as part of the team, led by US Senator Jeff Sessions, a Republican from Alabama who endorsed Trump last month.
Most of those named by Trump are not well known in foreign policy academic or expert circles.
Phares told Reuters he began advising Trump at the weekend. He previously had served as a national security adviser to former Republican presidential candidate Mitt Romney, who has roundly criticised Trump.
Schmitz was a Pentagon inspector general during the George W. Bush Administration and has worked for Blackwater Worldwide, a now-defunct private US security firm whose personnel were involved in a deadly shooting that killed Iraqi civilians in 2007.
Kellogg has considerable military experience, having served as the chief operating officer of the Coalition Provisional Authority, the US-run provisional government imposed on Iraq after the US-led invasion under Bush.
According to the Post, Papadopoulos previously advised Trump's former rival Ben Carson, who has now backed Trump.
Sessions, who in February became the first sitting US senator to endorse party front-runner Trump, is also not seen as an influential foreign policy or national security player in the US Congress.
Last week, Trump said in a television interview on MSNBC, which has been pressing the Republican front-runner to name his foreign advisory team, that he relies on his own instinct.
"I'm speaking with myself, number one, because I have a very good brain," he told MSNBC. "I know what I'm doing. ... My primary consultant is myself."