(CNN) White House officials are considering releasing a transcript of President Donald Trump's call with the Ukrainian President , multiple sources have told CNN, amid mounting scrutiny over the interaction.

However, some senior administration officials, such as Secretary of State Mike Pompeo and Treasury Secretary Steve Mnuchin, are against the idea because of the precedent releasing it could set with future foreign leaders. At particular issue: White House concern about giving Congress ammunition to demand transcripts of Trump's calls with Russian President Vladimir Putin.

Trump's acknowledgment that he discussed former Vice President Joe Biden in a July call with Ukraine's president has intensified scrutiny on his interactions and decisions on Ukraine.

On Friday CNN reported Trump pressed Ukrainian President Volodymyr Zelensky in the call to investigate former Vice President Joe Biden's son, Hunter, according to a person familiar with the situation. That call was also part of a whistleblower complaint submitted to the Intelligence Community Inspector General, another person familiar with the situation told CNN.

There is no evidence of wrongdoing by either Joe or Hunter Biden.

Trump remained unclear about the fate of the transcript on Monday, speaking about the Ukraine controversy multiple times during his visit to the United Nations General Assembly in New York.

"Perhaps you'll see it, perhaps you won't see that, it depends on what we want to do," Trump said of the transcript. The President again denied that he threatened to withhold aid to Ukraine unless the country's leaders did his bidding and investigated the Bidens.

"I did not make a statement that, 'You have to do this or I'm not going to give you aid.' I wouldn't do that. I wouldn't do that," he said.

But Trump again suggested he hoped to release a transcript of his conversation.

"It was a very nice call. I hope you get to see it and I hope you get to see it soon," he said.

More mixed signals

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House Democrats have demanded to see the full complaint a whistleblower filed last month with the intelligence community inspector general -- a document the administration, including the White House Counsel's Office and the Justice Department's Office of Legal Counsel -- has fought to keep secret. The complaint includes the Ukraine call, a source told CNN, but may not necessarily be limited to that one incident.

Over the weekend, White House officials solicited opinions from outside advisers about whether they should release the transcript of Trump's call with the Zelensky, as well as how advisers think the White House should message it if the transcript was "embarrassing."

A person familiar with the discussions said the White House Counsel's Office is currently involved in evaluating whether the transcript should be released and in what form. The source said the release could happen "soon."

But Stephanie Grisham, White House press secretary, sounded a reluctant note this morning on Fox News.

"I do think that perhaps releasing this kind of a transcript could set a bad precedent. He is willing to do it, I think. But there is a lot of other people, lawyers and such that may have a problem with it. So we will see what happens," Grisham said.

Officials are also looking at potential redactions of Zelensky's portion of the conversation.

On Saturday, Trump raised the possibility of releasing a transcript of the call to a "respected source" for review.

In March, White House counsel Pat Cipillone sent a letter to Congress saying the administration would not release any conversations Trump has had with foreign leaders, citing longstanding precedent. That letter came in the context of White House efforts to shield Trump's conversations with Putin. But releasing the Zelensky call could undermine the White House's pre-existing efforts to keep those Putin conversations secret, which is one of several concerns inside the White House over putting out details of the call.

'A terrible precedent'

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Another concern -- voiced on the Sunday shows by Pompeo and Mnuchin -- is that publishing the call could chill candor when Trump speaks with foreign leaders in the future. Both suggested Trump requires an expectation of privacy in order to conduct diplomacy effectively.

"I think that would be a terrible precedent," Mnuchin said Sunday on CNN's "State of the Union." "Conversations between world leaders are meant to be confidential, and if every time someone for political reasons raised a question, and all of a sudden those conversations were disclosed publicly ... then why would world leaders want to have conversations together?"

Pompeo echoed a similar reservation.

"We don't release transcripts very often. It's the rare case. Those are private conversations between world leaders, and it wouldn't be appropriate to do so except in the most extreme circumstances. There's no, there's no evidence that would be appropriate here at this point," Pompeo said on ABC's "This Week."

A number of political advisers have urged the White House to release it, with full knowledge of the diplomatic concerns cited by Mnuchin and Pompeo over the weekend.

"Otherwise, it looks like we're hiding something far more nefarious," one person said.

Republican Sen. Lindsey Graham, a staunch Trump ally, publicly urged Trump to publish the transcript on Monday and hinted the White House could do so in the days ahead.

"I would just urge the President ... to release as much as possible. And here's what I think -- I think you're going to find (out) more about that phone call in the coming days," Graham said during on appearance on Hugh Hewitt's radio show. "You're going to be surprised about the level of transparency regarding that phone call."

One senior administration official said there's an understanding inside the White House that the timing of the administration's suspension of the Ukraine aid, which came around the time of Trump's call with the Ukrainian president, "lends to a question of what was going on."

But this official, like the President, insists there was no quid pro quo.

Trump himself told reporters yesterday while leaving the White House that he wants to release the call. But he later said one way to release the call, given concerns about protecting American interests, would be to "give it to a respected source."

He said in Houston on Sunday that if the call was released, people would "see one of the finest, one of the nicest" conversations.