The likelihood of such a potential deal seems miniscule, as many Republicans have said they don't believe any witnesses are necessary and Democrats say Hunter Biden is irrelevant to hear from.
"I think we ought to go through the right process," the lawmaker from Florida said.
The president also said it would not be good to have someone testify who had left his administration on bad terms.
The Washington Post reported that the Trump administration is considering blocking possible public testimony from former National Security Advisor John Bolton on national security grounds.
"I think they [the Senate] should hear the testimony that they can get," Congressman Francis Rooney said.
"That directly contradicts what you said as a Republican House impeachment manager in 1999 during the Clinton impeachment trial," Chris Wallace noted.
Republicans for the Rule of Law will begin running advertisements during Fox News programming calling for the testimony of John Bolton during the impeachment trial.
Most GOP senators believe the deal with Ukraine the president tried to make was "improper" but not impeachable, the Fox News analyst said.
"Next to Donald Trump himself, this could be the most important witness that the Senate could call to determine what the actual facts are," a former Watergate prosecutor said.
The poll by Quinnipiac University also found just under four in 10 Republicans wanted the former national security adviser to appear before lawmakers at the trial.
The former GOP presidential nominee suggested he would vote in favor of hearing testimony from the former national security adviser.
Texas Rep. Dan Crenshaw also asked why House Democrats did not subpoena President Donald Trump's former national security adviser during the impeachment inquiry.
Andrew Napolitano cited "new emails of people getting instructions directly from the president to hold up on the sending of the [military] funds [to Ukraine]."
The former national security adviser is believed to have firsthand knowledge of the president's Ukraine dealings and his decision to withhold $400 million in military aid from the U.S. ally.
"We have ZERO problems with the American people...Our sole problem is Trump. In the event of war, it is he who will bear full responsibility," a top Iranian presidential adviser said on Twitter.
"Staying silent will only lead observers to infer that you care more about book royalties than, you know, who should be the president of the United States," Daniel W. Drezner wrote.
"Forgive me for being snarky and blunt, but he's stealing a page from Omarosa's playbook," Mark Groombrdige told CNN.
Bolton, whom Trump ousted from the position in September, wrote in a tweet that more "effective" policy would be needed to keep the United States and its allies safe from North Korea.
The former national security advisor said he does not think North Korea will ever voluntarily surrender its nuclear weapons, regardless of what Kim Jong Un tells Trump.
The House is expected to impeach the president in a vote on Wednesday, and Senate leaders are now wrangling to decide the format of the subsequent trial.
Senator Chuck Schumer says he expects "some" of his Republican colleagues to say "that's fair," when they read his letter.
A representative for Republicans for the Rule of Law told Newsweek that the group targeted representatives who have shown a willingness to "assert their independence" of the president.
The former national security adviser has so far refused to testify to House investigators, even threatening legal action if he is subpoenaed.
In a vague tweet, Bolton said that America's "commitment to our national security priorities" were "under attack from within," prompting some Twitter users to urge the former national security adviser to testify before the impeachment committee.
White House Press Secretary Stephanie Grisham has claimed that former National Security Advisor John Bolton may not understand "how Twitter works" due to his "advanced age," and is mistaken about his claim that the White House froze him out of his account.
"Glad to be back on Twitter after more than two months," Bolton tweeted Friday morning. "For the backstory, stay tuned........"
MSNBC anchor Nicolle Wallace claimed that the potential impeachment inquiry testimony of former national security adviser John Bolton could be "the difference between conviction and no conviction in the senate," during a panel discussion on Monday.
Former National Security Adviser John Bolton became the latest ex-Trump administration official to sign a book deal this week.
The former national security adviser John Bolton is expected to be a no-show on Capitol Hill today just as 'Abominable' will be a no-show in Malaysia after producers refused to follow orders from the country's censors.
"We know you're not in custody (yet)," Conway, who is married to Trump's senior counselor Kellyanne Conway, tweeted.