As senators questioned both the Trump legal team and the Democratic managers of the trial on Wednesday, Trump lawyer Alan Dershowitz offered an expansive defence of presidential power that provoked astonishment among Democrats.

"If a president does something which he believes will help him get elected in the public interest, that cannot be the kind of quid pro quo that results in an impeachment," Dershowitz said, referring to the charge that Trump abused his power by using congressionally approved security aid as leverage to get a foreign power to smear his political rival Joe Biden.

Democratic Senator Mazie Hirono told reporters: "That was one of the most bizarre things I've ever heard as a response."

Senator John Barrasso, the No.3 Republican in seniority, said it was possible the trial could end on Friday without witnesses being called, as Democrats want.

"The momentum is clearly in the direction of moving to final judgment on Friday. That vote will be Friday. We still have a couple members who said they want to listen to the answers to questions but that's where the momentum is," Barrasso said.

Asked when the vote might take place to settle the debate over witnesses and move to either acquit or convict Trump, Barrasso said probably Friday afternoon or late that day.

Other Republican senators were predicting a similar outcome.

The Democratic-led House of Representatives approved the two articles of impeachment being heard in the Republican-controlled Senate in December.

Democrats have sought to persuade at least four Republican senators to vote with them in favour of witnesses to assure a majority vote in the 100-seat chamber.

Democratic Senator Chris Coons was asked during a break if the Democrats' fight for witnesses was lost.

"I don't know that for sure one way or the other," he said but called the tone and questions of senators "not encouraging".

However, Senate Democratic leader Chuck Schumer said: "My gut tells me we're making progress, progress, progress."

While the Senate is expected to acquit Trump and leave him in office no matter what happens, allowing witnesses could inflict political damage on the president as he seeks re-election on November 3.

One such witness is former national security adviser John Bolton, who left the White House in September after several sharp disagreements with Trump over foreign policy.

The New York Times has reported that Bolton wrote in an as-yet unpublished book that the president told him he wanted to freeze $US391 million in security aid - passed by US Congress to help Ukraine battle Russia-backed separatists - until Kiev pursued investigations into Democrats, including Biden and the former vice president's son, Hunter.

On Wednesday, the White House objected to the book's publication. A January 23 letter from the White House National Security Council to Bolton's lawyer said the manuscript appeared to contain "significant amounts of classified information".

Democrats believe Bolton, a Republican foreign policy hawk, could help them solidify their case against the president and want to call him and a small number of other officials to testify.

Trump's fellow Republicans in the Senate have resisted the idea.

Bolton lawyer Charles Cooper said on Wednesday that neither he nor his client believed any information in a chapter on Ukraine "could reasonably be considered classified".

Trump lashed out at Bolton on Twitter on Wednesday, saying Bolton "couldn't get approved for the Ambassador to the UN years ago, couldn't get approved for anything since, 'begged' me for a non Senate approved job" and added that "if I listened to him, we would be in World War Six by now".

Responding to a question by top Senate Democrat Chuck Schumer, lead House prosecutor Adam Schiff said there would be no way to have a fair trial without witnesses.

Australian Associated Press