"I will absolutely bring that up. I don't think you'll have any, 'Gee, I did it. I did it. You got me.' There won't be a Perry Mason here, I don't think, but you never know what happens, right? But I will absolutely, firmly ask the question," Trump said. "And hopefully, we'll have a very good relationship with Russia."
Instead, the US President is setting his sights on establishing a new Strategic Arms Reduction Treaty (START) between the United States and Russia to continue decades of progressive nuclear disarmament between the two countries, the source told CNN. The source said Trump has been fired up about making progress on extending the US and Russia's denuclearization treaty, now known as New Start which is set to expire in 2021.
Trump sees progress on an arms control treaty as the likeliest area of progress for the Trump-Putin summit, the source said.
"The proliferation is a tremendous -- I mean, to me, it's the biggest problem in the world, nuclear weapons. Biggest problem in the world," Trump said on Friday. "So, we could do something to substantially reduce them -- I mean, ideally get rid of them. It's -- maybe that's a dream."
The White House declined a CNN request for comment.
But as Trump and Putin prepare to arrive in Helsinki, the source with knowledge of the discussions said there is still no set, organized agenda for the summit. Privately, Trump has also made clear that he is unsure how the summit will unfold and what the outcome will be, the source said.
The risks of the meeting, the source said, are if Trump offers something for free -- such as reducing US support for Ukraine or offers ambiguity on Crimea. Or if Trump's bonding with Putin emboldens Europeans who want to lift sanctions on Russia -- the new Italian government, Hungary or Austria.
Trump and US officials have made clear they intend to raise a series of issues during the Helsinki summit, from the ongoing civil war in Syria to Russian actions in Ukraine to cyberactivities and North Korea.
Trump believes his discussions with Putin on Syria could yield the crude beginnings of a deal, but any agreement would be very preliminary. Trump, who is eager to withdraw US troops from the country, would like for Russia to get the Iranians to pull out of Syria, according to the source, but many experts within and outside the administration see that as an unrealistic demand the Russians will not be able to deliver on.
On North Korea, Ukraine and cyber issues, the potential outcomes of Trump and Putin's talks seem less clear.
The source with knowledge of Trump's discussions said Putin is still eager to form a joint Russia-US cybersecurity unit, which remains unlikely. The source said it is possible Trump and Putin agree to a working-level dialogue on cybersecurity issues.
On North Korea, the source said Russian officials do not believe Trump's maximum pressure campaign has worked, but agree on the objective of nonproliferation and want to be involved in the denuclearization talks.
The United States, though, would rather continue its bilateral talks with North Korea. However, this source believes it's likely Putin will offer technical assistance, such as expertise in the removal of nuclear material and that Trump may well agree to Russian involvement in some way, which would also be something of a win for Putin.
White House keeps summit preparation under wraps
Ahead of his one-on-one with Putin, officials said Trump has spent the past two days preparing for the summit by meeting with advisers who traveled with him and phoning those who didn't. But aside from that, the White House been incredibly tight-lipped about the extent of the President's preparations.
"The President has had several phone calls with relevant stakeholders and was joined at Turnberry by aides and administration officials for multiple meetings," one White House official told CNN.
Another added, "In preparation for the meeting with Putin, President Trump has spoken with allies, discussed the issues with administration officials, and met with advisors while at NATO, in the U.K, and in Turnberry."
As he boarded Air Force One Sunday, national security adviser John Bolton was asked how the Putin preparations had gone. "Fine, thanks," he said, before turning and climbing the stairs.
Although US Ambassador to Russia Jon Huntsman held a call with reporters 10 days ago, in a departure from previous meetings with world leaders, the White House has not held a dedicated background briefing with reporters to preview the Putin meeting. As of Sunday night, none was scheduled, according to one official.
The White House did put two administration officials on television Sunday -- Bolton and Huntsman. During his interview with Chuck Todd, Huntsman insisted that Monday isn't a summit, but "a meeting" with Putin, noting to Todd that there is "no state dinner, no joint statement, no deliverables that are pre-packaged."
However, Trump later referred to it as a "summit" on Twitter.