(CNN) President Donald Trump's stance on Ukraine has evolved over the past year from one of general uninterest to a more engaged approach as he has discussed allegations of wrongdoing involving former Vice President Joe Biden and his son, people familiar with the matter said.

Now Ukraine has become wrapped in the Trump presidency's many subplots: the role of Russia and President Vladimir Putin, the legacy of Trump's predecessor Barack Obama, Trump's reelection outlook and a loose network of advisers not always operating in concert.

The result is renewed focus on a country Trump once sought to tune out but where he now sees a political opportunity. His approach to Ukraine melds political and national security concerns fanned by some of his closest advisers.

Trump has raised the issue involving the former vice president and his son Hunter Biden repeatedly in private conversations and believes there is a political opportunity in further probing the matter, the people familiar with the matter said.

He's been urged along by his private attorney, Rudy Giuliani, who told CNN on Thursday evening that he'd pressed Ukrainian officials to investigate Biden and his son. Giuliani has maintained that he has been acting on his own and not at the direction of the President as he meets with Ukrainian officials. But Giuliani is aware that the issue has gotten Trump's attention, according to the people familiar with the situation. And Trump has raised it multiple times, in person and on the phone.

A source close to the White House who is familiar with Trump's comments said the President has been seething for months about Ukraine and Biden. The source described Trump as "angry" about what he sees as a liability for the former vice president. The source also said Giuliani has been "egging him on."

Trump told reporters on Friday that "somebody ought to look into" the Biden matter, and said that "it doesn't matter what I discussed" during a July phone call with Ukrainian President Volodymyr Zelensky. CNN reported on Friday that in that call, Trump pressed Zelensky to investigate Biden's son . Trump is due to meet next Wednesday with Zelensky in New York.

Trump was not initially interested in meeting with Zelensky or engaging with him, viewing him as an extension of the country's previous leader, President Petro Poroshenko. Trump believed Ukraine was a corrupt country that wasn't committed to reform, according to people familiar with his thinking at the time.

The phone call and meeting come after months of back and forth between Trump and his advisers, who have worked to convince him that engaging the new Ukrainian leader is worth his time and effort for national security reasons.

The country's attacks on Trump's former campaign chairman Paul Manafort, with accusations of him laundering money with offshore accounts, were the ultimate foundation for the President's beliefs.

Trump also consistently cast Ukraine -- a portion of which was annexed by Russia in 2014 -- as a messy situation created by his predecessor that he was unenthusiastic about wading into himself.

"He had never been concerned or interested in Ukraine," one person familiar with Trump's thinking said.

"Obama lost it," was Trump's view, the person said, adding that the President always seemed "more interested in engaging Putin than Zelensky."

Trump's ties to Putin have been heavily scrutinized, and he's been accused of showing deference to the Russian leader. He's also remained fixated on Obama, frequently seeking to unravel his legacy.

That lack of interest in Ukraine appeared to shift over the summer, when some of Trump's national security advisers worked to convince him that engaging Ukraine's new leader would benefit US national security interests. Though Trump continued to remain skeptical, he told his advisers he was open to being convinced of further engagement.

Then-national security adviser John Bolton and other senior Trump administration officials invited Oleksandr Danylyuk, the secretary of Ukraine's National Security and Defense Council, to Washington for meetings in early July. They went well, and the White House saw it as a "sign of encouragement" to nudge Trump toward working with Ukraine.

The renewed engagement happened to dovetail with Giuliani's efforts to convince Ukrainian officials to look into Biden and his son -- an effort Giuliani spoke about publicly and that quickly caught Trump's attention. Even before Zelensky took office, Giuliani made known he was looking to set up a meeting to discuss an investigation into Burisma, the natural gas company where Biden's son Hunter had served on the board of directors.

Giuliani's meetings occurred over the summer, just as US administration officials were working to spark Trump's interest in Ukraine. The parallel efforts seemed to be the launchpad for convincing Trump to engage with Ukraine more robustly. Three weeks later, Trump spoke by phone with Zelensky for the first time, in a call that is now under intense scrutiny for its potential role in the whistleblower's complaint . Later, aides worked to arrange a meeting in Poland, though Trump ultimately did not make the trip because of a hurricane in the United States.

People familiar with the matter said Bolton and the other US officials who met with Danylyuk in early July did not discuss the Biden matter. But the issue was known, and colored the talks.

"That was a bizarre situation, but it all seemed to be dealt with in Giuliani track," a person familiar with the meetings said. "It was out there, but it was being handled by Giuliani. We did not deal with that because he [Giuliani] was talking about it and saying he was a private citizen."

At the same time, the administration begin reviewing $250 million in foreign aid to Ukraine, initially placing a hold on the package that angered some in Congress. The issue provided another wedge between Bolton, who was an advocate for the aid, and acting chief of staff Mick Mulvaney, who pushed for the package to be reviewed. The money was released last week

It's not known how, if at all, the foreign aid was related to the Biden matter. And a person familiar with the situation said Friday that Trump had not discussed the pending aid package during the July 25 call with Zelensky.

But even before this week's revelations about the intelligence whistleblower, Democrats in Congress had accused the administration of engaging in a quid pro quo with the Ukrainian government.

Through it all, Trump's interactions and meetings on Ukraine have been treated with special sensitivity within the administration. The State Department never got extensive readouts of his calls. And few people within the administration learned precisely what was discussed.

"There was concern about leaks," one person said of the tight hold on information.