Trump triggered consternation -- and widespread condemnation -- when he made an unprecedented campaign threat to jail his Democratic rival should he win the White House.
The Republican made Clinton's email scandal and allegations of pay-to-play at her family foundation core themes of his campaign, railing against her "crimes" and leading fired-up supporters in chants of "Lock her Up!"
But since his election he has deflected questioning on the subject, saying in an interview he would think about it, but had other priorities as incoming head of state.
MSNBC, which first reported that Trump would not push for further investigation of Hillary Clinton, said Trump aide Kellyanne Conway confirmed it.
"I think when the president-elect... tells you before he's even inaugurated that he doesn't wish to pursue these charges, it sends a very strong message, tone and content" to fellow Republicans, she told MSNBC's "Morning Joe."
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Rudy Giuliani, a vice chairman of Trump's transition team, told reporters a decision not to investigate would be consistent with a US tradition "that after you win an election, you sort of put things behind you."
"And if that's the decision he reached, that's perfectly consistent with sort of a historical pattern of things come up, you say a lot of things, even some bad things might happen, and then you can sort of put it behind you in order to unite the nation," Giuliani said.
"So if he made that decision, I would be supportive of it. I'd also be supportive of continuing the investigation. I think the president-elect had a tough choice there, you could go either way."
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'Because you'd be in jail'
During their second presidential debate in October, Trump told Clinton that, if elected, he would instruct his attorney general to get a special prosecutor to look into her email practices when secretary of state.
Clinton responded: "It's just awfully good that someone with the temperament of Donald Trump is not in charge of the law in our country."
Trump then quipped: "Because you'd be in jail."
Helping Clinton heal?
It would be highly unusual, if not unprecedented, for a sitting president to direct his attorney general to name a special prosecutor to investigate a political rival.
Although many of Trump's fervent supporters might see a decision not to investigate as a broken promise, it also would open Trump to accusations of abuse of power.
Conway said Clinton "still has to face the fact a majority of Americans don't find her to be honest or trustworthy."
"If Donald Trump can help her heal, perhaps that's a good thing," she added.
"He's thinking of many different things as he prepares to become the president of the United States, and things that sound like the campaign aren't among them."
Clinton has attributed her loss to the bombshell decision by FBI Director James Comey to re-open the probe into her use of a private email server, less than two weeks before the vote.
In a call with donors, she claimed that two letters Comey sent to Congress -- re-opening the probe and closing it again after finding no new evidence of wrongdoing -- had tilted crucial states towards her Republican rival.
Comey's second letter, sent three days before the election, stated that the FBI maintained its July recommendation not to charge Clinton.
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