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.