Former New York City Mayor Rudy Giuliani has an "enormous skill set" that would serve him well in any part of a Donald Trump administration, and he "could be" tapped to serve as secretary of state, senior adviser Kellyanne Conway said Tuesday.

"He certainly is a very close adviser of President-elect Trump's," Conway, smiling widely, told NBC's "Today" show. "The mayor has enormous skill set. He would be an excellent member of the cabinet and that's where I'll leave it."

While speaking Wall Street Journal CEO Council event Monday night in Washington, Giuliani, also a former federal prosecutor, said he will not become the attorney general, but when it came to the job of secretary of State, he was more guarded.

He commented that former ambassador to the United Nations John Bolton would be a very good choice, but when asked if there was anyone better, he responded "maybe me, I don't know."

Conway, who was Trump's campaign manager and is widely credited for her role in his win, said she also spoke at the same event. However, she was also guarded Tuesday about her own future with the Trump administration.

When asked how she'd be introduced in two weeks in her media appearances, she suggested that "Today" should refer to her as "Kellyanne Conway, who's very happy that President-elect Trump was elevated to this position."

And as for her exact title, that would be under the "to be determined" status.

"President-elect Trump has been incredibly generous in discussing that with me," she told anchors Matt Lauer and Savannah Guthrie. "I'm sure a lot of your viewers can relate, I didn't see mom of four young children in any of the job descriptions. I am trying to navigate my best and highest use...along with the personal demands on my time and my life."

She was more open, however, about Trump's choice of former Breitbart executive Steve Bannon as his chief strategist.

"I promise you, he's not as scary, and he is as brilliant a tactician and our campaign general, frankly, on the field as everyone is also saying," Conway said. "I know him well. I work hand in glove with him. I feel that these charges are very unfair."

Conway, during the campaign and after, became the public face of Trump's campaign team, but that was a decision she said was made "strategically."

"They put me out there all the time," she said. "I would love to share the stage with him and others, believe me. But at the same time, you have to realize, I get a lot of credit for managing this campaign, and that's nice, but we were a very solid team focused, cohesive, and, frankly, very much in agreement with the strategy. He was a big part of that."

Bannon, she continued, believes in Trump's vision and is there to support that, but "not everybody wants to be a public face. Not everybody is asked to do that on behalf of the president-elect."

She also noted Tuesday there have been many questions about the Trump transition, including speculation security clearances are being sought for his adult children.

"I'm sure that the Trump children will be there to support their father in informal capacities and I think these are just regular inquiries among many that are made when folks are transitioning into a new administration for the Trump family, a new city," she said.

Conway also lauded President Barack Obama for saying Monday he believes Trump to be pragmatic and practical, rather than "ideological."

"I agree with President Obama's assessment about President-elect Donald Trump completely, and I am very thrilled that the president would tell the country that because it is an important voice to have out there right now," Conway said. "Those who spend a little bit of time beyond the caricatures, beyond the ridicule and get to know Donald Trump and listen to his message will come to a similar conclusion."