The Trump team has added a name to its list of potential candidates for secretary of defense — outgoing Sen. Kelly Ayotte (R-N.H.), according to two sources familiar with the ongoing discussions. If chosen, Ayotte would stand out in a Trump administration as a neoconservative defense hawk and one of the few women in the incoming Trump Cabinet.

No decisions have been made and the current list for possible defense secretary picks still centers around retired Army Lt. Gen. Joseph “Keith” Kellogg, former Defense Intelligence Agency director Gen. Mike Flynn and Sen. Jeff Sessions (R-Ala.). Flynn would need a congressional waiver to bypass a law that requires any defense secretary to be seven years out of active duty service before taking command of the Pentagon.

But Ayotte’s name has surfaced in internal discussions as a potential olive branch to the GOP foreign policy establishment that the Trump campaign was often at odds with over the past year. Ayotte is regarded as knowledgeable and competent, sources familiar with the discussions said, and would surely get swift Senate confirmation.

The Trump-Ayotte relationship has been a roller coaster over the past several months, as Ayotte tried to balance between supporting her party’s nominee and placing distance between her campaign and Trump’s more controversial comments, especially regarding women.

Ayotte did not attend the Republican National Convention in Cleveland in July. During one of her debates, she said Trump was “absolutely” a role model for children and later said she “misspoke.” After Trump’s lewd comments about women were exposed on the Access Hollywood tape, Ayotte announced she would cast a write-in vote for Mike Pence, saying “I cannot and will not support a candidate for president who brags about degrading and assaulting women.”

On Thursday, my colleague Jennifer Rubin explained the upside for Trump in adding Ayotte to his team:

Her elevation would signal that Trump campaign cronies won’t be moving into the West Wing — or the Pentagon; Trump would get credit for selecting a mainstream, serious person. In one stroke, Trump could dispel the notion that he is a lackey for Russian President Vladimir Putin or an isolationist. Ayotte would be an ideal personality to smooth out the relationship between Trump and the generals whom he routinely insulted.

Trump has often criticized the neoconservative wing of the Republican party as too quick to intervene abroad and responsible for costly U.S. interventions such as the Iraq War. But going forward, Trump has promised to ramp up the war against the Islamic State and other terrorist groups in the Middle East and hawks such as Ayotte support such a policy.

There are also several other areas of national security where Trump and conservative hawks in Congress plan to work together, including stepping up pressure on Iran, getting rid of the sequester on defense funding to increase military spending and increasing aid to Israel.

The question is whether Trump’s desire to build a big tent for national security conservatives will outweigh his disdain for the neocons in the Senate that Ayotte is associated with.

“She’s viewed as being in the mainstream of conservative Republican foreign policy,” one GOP foreign policy official told me. “She would be a defense secretary in the mold of John McCain or Lindsey Graham, and if that’s what Donald Trump is looking for, that’s what he’s going to get.”