"I'm going to think about it," he said. "I don't want to hurt them, I don't want to hurt them. They're, they're good people."
It is traditional in American politics that after someone wins an election, the victor puts some of the campaign rhetoric behind them, and Trump's decision would be consistent with that sort of historical pattern.
The president-elect's new position, however, stands in contrast with leading members of his party. Jason Chaffetz, the Utah congressman finishing his first term leading the powerful House Oversight and Government Reform Committee, has vowed to continue to investigate Clinton's email server.
"It would be totally remiss of us to dismiss [the email investigation] because she's not going to be president," Chaffetz said after the election, referring to the defeated Democratic nominee.
While FBI director James B. Comey has repeatedly said the bureau did not find enough evidence to recommend prosecuting Clinton over the email issue, he questioned her judgment in using a private server, calling it "extremely careless".
Legal experts say any attempt by Trump to influence whether or not an investigation would be pursued threatens the integrity of the justice system.
"The President-elect has demonstrated his complete lack of understanding of how the government makes these kinds of decisions," said Stephen Vladeck, a law professor at the University of Texas at Austin. "The attorney general answers to the president, but the department is supposed to be independent, especially when it comes to prosecutorial decisions. Any president, especially our next president, needs to both understand and respect that - or else they risk politicising criminal prosecutions in ways that can be damaging."
On the policy front, Trump released a video late Monday in which he said his transition to power, which has at times been chaotic, "is working very smoothly, efficiently and effectively."
He outlined a series of executive actions in the video that he said he intends to take on his first day in office: issuing notification of intent to withdraw from the Trans-Pacific Partnership trade agreement; canceling restrictions on energy production; putting in place a rule that two regulations must be eliminated for every new one enacted; ordering a plan to protect US infrastructure from cyberattacks and other forms of attack; directing the Labor Department to investigate "abuses of visa programs that undercut the American worker"; and imposing a five-year ban on executive officials becoming lobbyists.
Notably missing from the actions were some of his most prominent campaign promises, such as building a wall along the US-Mexican border to keep out illegal immigrants and developing an early plan to confront the Islamic State terror group.
Though Trump's first five picks for top jobs in his administration have all been white men, transition officials insisted on Monday that the team he ultimately puts together will represent a cross-section of America.
Trump spokesman Jason Miller told reporters on a conference call that the President-elect met with a "high-calibre and broad and diverse group" of job seekers and advisers in recent days and predicted that the top rungs of the executive branch that Trump assembles in the coming weeks "will be very broad and diverse, both with the Cabinet and the administration".
That point was echoed by Conway, who said that assuring diversity - both in backgrounds and political philosophy - is a priority for Trump.
"And diversity means meeting with people across the aisle who are traditionally more Democratic, who are coming together and wanting to offer him advice, perhaps vie for a spot in his Cabinet," Conway said. "But willing to give him counsel and willing to share experiences and have candid conversations about their views and their backgrounds."
The Trump aides were seeking to dismiss speculation that the parade of people summoned by the president-elect - which has included women, nonwhites and erstwhile political foes - has been merely for show.
That skepticism comes in the aftermath of a brutal presidential campaign that was punctuated by frequent incidents in which Trump said and did things that offended women, Latinos and Muslims, while drawing support from white nationalist groups.
Exit polls suggest that Trump owes his victory to white voters, of whom 58 per cent supported him. By comparison, he won only 8 per cent of African American voters, and 29 per cent each of Hispanics and Asian Americans, the exit polls showed.