Washington (CNN) In the months leading up to President Donald Trump's July 25 phone call with Ukrainian President Volodymyr Zelensky , multiple people associated with Trump, both inside and outside of his administration, were engaged in efforts to change leadership at Naftogaz, Ukraine's geopolitically important state-owned oil and gas company.

One of those people, US Energy Secretary Rick Perry , faces a deadline Friday to comply with a congressional subpoena as part of the ongoing impeachment inquiry.

Questions about whether Trump offered to restore military aid in exchange for politically beneficial investigations in Ukraine have formed the basis of the impeachment inquiry. But the parallel attempts to influence Naftogaz further illustrate the nature of the Trump administration's interactions with Ukraine, in which statecraft and diplomacy appear to be mixed up with political and business interests and which are now the focus of a federal criminal investigation.

The common thread in these attempted shakeups of Naftogaz is Rudy Giuliani, Trump's personal attorney who has emerged as a central player in US-Ukraine relations.

Among those pushing for changes at Naftogaz was Perry. During his May trip to Kiev for Zelensky's inauguration, Perry delivered a list of four candidates to replace the existing American member of Naftogaz's international supervisory board, according to a source familiar with Perry's conversations.

Two months earlier, Naftogaz was also in the crosshairs of two associates of Giuliani, Lev Parnas and Igor Fruman. Parnas and Fruman were pushing a scheme at a major energy conference in Houston to replace Naftogaz's chief executive officer with someone who would be more beneficial to their own business interests, according to one American businessman informed of their efforts.

The two Florida-based businessmen, who have given more than $300,000 to pro-Trump and Republican political committees, were indicted for campaign-finance violations last week. Some of those potential violations concern donations made through a company controlled by Parnas and Fruman called Global Energy Partners.

Parnas and Fruman aided Giuliani's efforts to dig up dirt on Trump's political opponents in Ukraine. Secretary Perry, meanwhile, has said he has discussed Ukrainian corruption with Giuliani. "I had a conversation with, a phone call with Rudy Guiliani about it," Perry said in an interview with the Christian Broadcasting Network earlier this month.

CNN has also reported that in late May Trump directed Perry to speak with Giuliani -- a private citizen -- about whether Zelensky was someone Trump could trust and engage with.

Giuliani denied he talked to Perry or anyone else about Naftogaz. "I don't know a damn thing about Naftogaz except that it exists," he told CNN.

Perry, Parnas, Fruman and Giuliani have all been subpoenaed by House Democrats for information relating to the impeachment inquiry. The deadline for Perry to comply is Friday.

Furthermore, potential changes at the Ukrainian energy giant could have major geopolitical implications. Gazprom, Russia's own state-owned energy corporation, has a contract with Naftogaz to move product through its pipelines in Ukraine.

"Naftogaz's pipeline system transfers half of Russian oil to Europe," said Ed Chow, an energy expert at the Center for Strategic and International Studies, a bipartisan think tank in Washington. "It's a strategically important company to the Ukrainian economy but also for the Ukrainian state."

That contract with Russia's Gazprom concludes at the end of the year and is currently up for renegotiation. The construction of the Nord Stream 2 pipeline, a controversial expansion of the existing pipeline between Russia and Germany, also threatens to cut Ukraine out of a big chunk of the European natural gas market.

"It's always hard to decipher Russia's intentions," said Richard Morningstar, the chairman of the Global Energy Center at the Atlantic Council. "But an unsettled Ukrainian energy situation makes it easier for them to convince the Europeans they can't trust Ukraine to move natural gas. "

Perry's list

In May, according to a former US official involved in Ukraine, Perry provided names to Ukrainian officials as potential replacements for the American member of the Naftogaz supervisory board.

The board was developed in coordination with the United States and other Western countries during the Obama administration to provide oversight and guard against corruption, a concern in the region, the former official explained. Three members are appointed by the Ukrainian government and four are recommended by the United States and the European Union through consultation with organizations like the International Monetary Fund and the European Bank for Reconstruction and Development. The Ukrainian government must approve the international members, who currently are American, British, French and Canadian, according to the company's website

Perry's goal, the former official believed, was to replace the current American representative, Amos Hochstein, with someone more known and favorable in Republican circles.

The official said Perry perceived Hochstein, a former diplomat, as an "Obama/Biden" guy in Ukraine. Hochstein is an executive for a Houston-based natural gas company and remains on the Naftogaz board. Hochstein did not provide comment for this story.

At a press conference in Lithuania last week, Perry disputed he was advocating for specific people to be placed on the board.

"That was a totally dreamed up story the best I can tell," he said. "We gave recommendations at the request of the Ukrainian government and will continue to."

An Energy Department official also disputed this characterization of Perry's list of names, telling CNN Perry was only recommending people who might be helpful for the new government to speak with about reforming Ukraine's energy sector.

Naftogaz representatives did not respond to a request for comment.

A possible shakedown

The Energy Department did not say whether Perry, who as secretary has been deeply involved with Ukraine and its critical energy industry, was aware of the activities of Parnas and Fruman to influence Naftogaz on the management level.

In March, the two Soviet-born Americans attended CERAWeek, a large annual energy conference in Houston. In a dinner meeting during the conference, Parnas and Fruman made their pitch to oust Naftogaz CEO Andriy Kobolyev to a senior Naftogaz executive, Andrew Favorov. That is according to Dale Perry, an American energy consultant operating in Ukraine who did not attend the meeting. (Dale Perry and Rick Perry are unrelated).

Dale Perry said he has for years been traveling to Ukraine once a month for business and told CNN that he and Favorov are former business partners who remained in touch, and that Favorov called him sometime in mid-April to tell him about the alarming conversation.

By Dale Perry's account, Parnas and Fruman appeared to have inside information about the Trump administration's approach to Ukraine. He said Favorov told him these men also said Trump would be replacing the US ambassador to Ukraine, Marie Yovanovitch , shortly. Parnas and Fruman suggested to Favorov that Trump would nominate a new ambassador more amenable to the two men's interest in breaking into the Ukrainian energy market.

It is unclear how Parnas and Fruman knew any information about the ambassador, but just two months later -- on May 20 -- Trump recalled Yovanovitch.

Dale Perry told CNN that shortly after hearing from Favorov in mid-April he wrote up a memo about what he heard and delivered it to a diplomat named Suriya Jayanti at the US embassy in Kiev. Perry provided the memo to the Associated Press, which first reported on this effort , but declined to share the memo with CNN.

A person with knowledge has told CNN that the House committees investigating impeachment have scheduled a deposition from Jayanti for later this month. The State Department did not respond to questions about the memo or Jayanti.

The idea from Parnas and Fruman, Dale Perry said, was for Favorov to take over the company. Perry said Parnas and Fruman also brought up Ukrainian businessman Dymtro Firtash, who has served as the main intermediary between Naftogaz and Gazprom. Parnas and Fruman mentioned Firtash's concern that Naftogaz owed him money and that the new CEO could potentially make that payment.

A spokesman for the law firm representing Firtash, diGenova and Toensing, said it had hired Parnas earlier this year as a "translator" but denies Firtash had a business relationship with Parnas, saying the two did not meet until June 2019.

"No money has been paid to Mr. Parnas by Mr. Firtash beyond his work as a translator for the law firm," said Mark Corallo, the firm's spokesman. Corallo also said the firm never hired Fruman and that he has no knowledge of any debt owed by Naftogaz to Firtash, saying that goes beyond the firm's representation of Firtash.

But the discussion of Firtash in Houston raises questions about whether Parnas and Fruman were connected to the deep-pocketed Ukrainian power broker.

Perry said Favorov told him he was concerned about the nature of the offer, likening it to a shakedown of management that also had little chance of success. He added that Favorov told him he had rejected the idea outright.

Favorov declined to respond to questions from CNN. A lawyer for Parnas and Fruman did not return a request for comment. A lawyer for a different man who was also at the meeting with Parnas, Fruman and Favorov confirmed the meeting took place.

Secretary Perry attended the Houston conference, delivering a speech about the United States' support for "the rule of law" and opposition to "using energy to coerce any nation." There is no indication the Secretary attended the meeting with Parnas, Fruman, Sargeant, and Favorov, nor that he knew anything about it.

During these events, a possible shakeup at Naftogaz was a live issue in Ukrainian politics, as well. Ukraine's prime minister at the time, Volodymyr Groysman, had moved on his end to remove the Naftogaz CEO. Groysman, an ally of the then-president Petro Poroshenko, pushed forward a resolution, approved on March 6 , allowing the government to fire and hire the CEO of Naftogaz without the input of the company's supervisory board.