"I think it's a tough decision," Giuliani told CNN's Chris Cuomo on "New Day." "I think it's a tough one that should be given a lot of thought and shouldn't be an off-the-cuff answer. Equal administration of justice is one of our most important principles."
He added: "It's been a tradition in our politics to put things behind us. On the other hand, you have to look at how bad was it? Because suppose somebody comes along a year from now and is alleged to have stolen $50,000 from a charity -- and (Clinton) was never investigated for hundreds of millions."
Giuliani told Cuomo he isn't interested in returning to government, but when asked whether he would accept the position of attorney general if it came with the condition of not going after Clinton, he said, "I think that's a presidential decision."
"We would have to talk about that. We would have to talk about what the -- what the ramifications of that to other prosecutions, future prosecutions -- how would you cover that, suppose more evidence came forward a year from now that we don't know now that makes it a much worse situation," the former New York City mayor said.
"Do you believe that the value of that investigation is worth the political instability it would cause?" asked Cuomo.
"I told you, I think it's a very close question. I think that somebody should review that very carefully, as to how bad is that evidence. And if it isn't as bad as some of the exaggerators think it is, then maybe the best thing to do is forget about it and move on. If it is really bad, then somebody's got to look at it who is independent," Giuliani said.
Christie, who has headed Trump's White House transition team and is reportedly under consideration for attorney general or chief of staff, was also noncommittal when asked about Clinton's future in an interview on NBC's "Today" show Thursday.
"I haven't spoken to (Trump) about that. I will tell you they had an enormously gracious conversation with each other Tuesday night," he said. "Again, politics are over now, people have spoken, time to move on."
"People wanted (Clinton) to be locked up. Those are his constituents," host Matt Lauer replied.
"Listen, but the people get to speak through their vote and they voted for Donald Trump to be president of the United States. It is now his job -- and I am confident he will -- to bring the country together," Christie said.
Both men were asked about their political futures under a Trump administration.
Giuliani -- a former associate US attorney general under President Ronald Reagan -- tried to downplay speculation, saying he would consider the job of attorney general "if it really was just me and I couldn't point to three others that would be just as good or better."
"I certainly have the energy, and there's probably nobody that knows the Justice Department better than me," he said, adding, "Christie is an excellent choice for any job in government."
And when Christie was asked on NBC if he was interested in being either chief of staff or attorney general, he delivered what NBC co-host Savannah Guthrie called a "pregnant pause."
"You don't really think I'm answering any of these questions, do you? You know me better than that," Christie said. "The answer is I'm not committed to doing anything in a new administration or not. The bottom line is that I have a job to do to help get the administration ready."
He added: "If there's some role for me that I want to do and that the President-elect wants me to do, you know, we've known each other for 14 years. We'll talk about it."